MAT180-HY1 Calculus 1

The function f(x)=2x3−24x2+72x+9f(x)=2x3-24x2+72x+9 has one local minimum and one local maximum. This function has a local minimum at xx equals     with value     and a local maximum at xx equals     with value    

Question 1. Last Attempt:  0 out of 1 (parts:  0/0.25,  0/0.25,  0/0.25,  0/0.25) Score in Gradebook:   0 out of 1 (parts:  0/0.25,  0/0.25,  0/0.25,  0/0.25)

The function f(x)=2x3−39x2+240x−2f(x)=2x3-39x2+240x-2 has two critical numbers. The smaller one is x=x=     and the larger one is x=x=     .

Question 2. Last Attempt:  0 out of 1 (parts:  0/0.5,  0/0.5) Score in Gradebook:   0 out of 1 (parts:  0/0.5,  0/0.5)

The function f(x)=2x3−27x2+84x+11f(x)=2x3-27x2+84x+11 has derivative f'(x)=6x2−54x+84f′(x)=6x2-54x+84. f(x) has one local minimum and one local maximum. f(x) has a local minimum at xx equals     with value     and a local maximum at xx equals     with value    

Question 3. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

The function f(x)=−2x3+42x2−240x+4f(x)=-2x3+42x2-240x+4 has one local minimum and one local maximum. This function has a local minimum at xx =     with value     and a local maximum at xx =     with value    

Question 4. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=−4x2+8x−3f(x)=-4x2+8x-3. f(x)f(x) is increasing on the interval (−∞,A](-∞,A] and decreasing on the interval [A,∞)[A,∞) where AA is the critical number. Find AA     At x=Ax=A, does f(x)f(x) have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER. 

Question 5. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

The function f(x)=8x+2x−1f(x)=8x+2x-1 has one local minimum and one local maximum. This function has a local maximum at x=x=     with value     and a local minimum at x=x=     with value    

Question 6. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

The function f(x)=(7x+2)e−3xf(x)=(7x+2)e-3x has one critical number. Find it. x =    

Question 7. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Mark the critical points on the following graph.

12345-1-2-3-4-54812-4-8-12-16-20

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Question 8. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Mark the critical points on the following graph.

1234-1-2-3-424-2-4-6-8-10-12-14-16

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Question 9. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Mark the critical points on the following graph. x4e−x28x4e-x28, 4

12345-1-2-3-4-548121620242832

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Question 10. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Find the critical numbers of the function f(x)=−12x5−45x4+80x3+4f(x)=-12x5-45x4+80x3+4 and classify them. x =  is a      x =  is a      x =  is a     

Question 11. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=−4x2+10x−7f(x)=-4x2+10x-7. f(x)f(x) has a critical point at x=x=    . At the critical point, does f(x)f(x) have a local min, a local max, or neither?     

Question 12. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

The function f(x)=2x3−36x2+120x+7f(x)=2x3-36x2+120x+7 has one local minimum and one local maximum. This function has a local minimum at xx equals     with value     and a local maximum at xx equals     with value    

Question 13. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

The function f(x)=2x3−36x2+120x+9f(x)=2x3-36x2+120x+9 has derivative f'(x)=6x2−72x+120f′(x)=6x2-72x+120. f(x) has one local minimum and one local maximum. f(x) has a local minimum at xx equals     with value     and a local maximum at xx equals     with value    

Question 14. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

The function f(x)=−2x3+33x2−108x+4f(x)=-2x3+33x2-108x+4 has one local minimum and one local maximum. This function has a local minimum at xx =     with value     and a local maximum at xx =     with value    

Question 15. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=−4x2+4x−2f(x)=-4x2+4x-2. f(x)f(x) is increasing on the interval (−∞,A](-∞,A] and decreasing on the interval [A,∞)[A,∞) where AA is the critical number. Find AA     At x=Ax=A, does f(x)f(x) have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER. 

Question 16. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

The function f(x)=(8x−8)e−5xf(x)=(8x-8)e-5x has one critical number. Find it. x =    

Question 17. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Mark the critical points on the following graph.

12345-1-2-3-4-5714212835-7-14-21-28

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Question 18. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Mark the critical points on the following graph.

12345-1-2-3-4-5-6-12-18-24-30-36-42-48-54-60

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Question 19. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Mark the critical points on the following graph. x1e−x27x1e-x27, 0.4

123-1-2-30.40.81.21.62-0.4-0.8-1.2-1.6-2

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Question 20. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Find the critical numbers of the function f(x)=6x5−15x4−20x3+1f(x)=6x5-15x4-20x3+1 and classify them. x =  is a      x =  is a      x =  is a     

Question 21. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=−4x2+6x−2f(x)=-4x2+6x-2. f(x)f(x) has a critical point at x=x=    . At the critical point, does f(x)f(x) have a local min, a local max, or neither?     

Question 22. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

The function f(x)=2x3−27x2+84x+5f(x)=2x3-27x2+84x+5 has one local minimum and one local maximum. This function has a local minimum at xx equals     with value     and a local maximum at xx equals     with value    

Question 23. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

The function f(x)=2x3−36x2+210x+10f(x)=2x3-36x2+210x+10 has derivative f'(x)=6x2−72x+210f′(x)=6x2-72x+210. f(x) has one local minimum and one local maximum. f(x) has a local minimum at xx equals     with value     and a local maximum at xx equals     with value    

Question 24. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

The function f(x)=−2x3+33x2−144x+1f(x)=-2x3+33x2-144x+1 has one local minimum and one local maximum. This function has a local minimum at xx =     with value     and a local maximum at xx =     with value    

Question 25. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=−3x2+8x−1f(x)=-3x2+8x-1. f(x)f(x) is increasing on the interval (−∞,A](-∞,A] and decreasing on the interval [A,∞)[A,∞) where AA is the critical number. Find AA     At x=Ax=A, does f(x)f(x) have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER. 

Question 26. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

The function f(x)=(3x−3)e−6xf(x)=(3x-3)e-6x has one critical number. Find it. x =    

Question 27. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Mark the critical points on the following graph.

12345-1-2-3-4-54812-4-8-12-16-20

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Question 28. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Mark the critical points on the following graph.

123-1-2-3123456

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Question 29. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Mark the critical points on the following graph. x4e−x25x4e-x25, 1

12345-1-2-3-4-51234567891011121314

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Question 30. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Find the critical numbers of the function f(x)=12x5−75x4−100x3−5f(x)=12x5-75x4-100x3-5 and classify them. x =  is a      x =  is a      x =  is a     

Question 31. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=−5x2+2x−2f(x)=-5x2+2x-2. f(x)f(x) has a critical point at x=x=    . At the critical point, does f(x)f(x) have a local min, a local max, or neither?     

Consider the function f(x)=6√x+4f(x)=6x+4 on the interval [2,6][2,6]. Find the average or mean slope of the function on this interval.     By the Mean Value Theorem, we know there exists a cc in the open interval (2,6)(2,6) such that f'(c)f′(c) is equal to this mean slope. For this problem, there is only one cc that works. Find it.    

Question 1. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=4x3−2xf(x)=4x3-2x on the interval [−3,3][-3,3]. Find the average or mean slope of the function on this interval.     By the Mean Value Theorem, we know there exists at least one cc in the open interval (−3,3)(-3,3) such that f'(c)f′(c) is equal to this mean slope. For this problem, there are two values of cc that work. The smaller one is     and the larger one is    

Question 2. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=1xf(x)=1x on the interval [1,7][1,7]. Find the average or mean slope of the function on this interval.     By the Mean Value Theorem, we know there exists a cc in the open interval (1,7)(1,7) such that f'(c)f′(c) is equal to this mean slope. For this problem, there is only one cc that works. Find it.    

Question 3. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=2x3−15x2−36x+10f(x)=2x3-15x2-36x+10 on the interval [−6,7][-6,7]. Find the average or mean slope of the function on this interval.     By the Mean Value Theorem, we know there exists a cc in the open interval (−6,7)(-6,7) such that f'(c)f′(c) is equal to this mean slope. For this problem, there are two values of cc that work. The smaller one is     and the larger one is    

Question 4. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Multiply: 37⋅101137⋅1011 Enter your answer as a single, reduced fraction

   

Question 5. Last Attempt:  1 out of 1 Score in Gradebook:   1 out of 1

Consider the function f(x)=4x3−4xf(x)=4x3-4x on the interval [−3,3][-3,3]. Find the average or mean slope of the function on this interval.     By the Mean Value Theorem, we know there exists at least one cc in the open interval (−3,3)(-3,3) such that f'(c)f′(c) is equal to this mean slope. For this problem, there are two values of cc that work. The smaller one is     and the larger one is    

Question 6. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=7−7x2f(x)=7-7x2 on the interval [−2,3][-2,3]. Find the average or mean slope of the function on this interval, i.e. f(3)−f(−2)3−(−2)=f(3)-f(-2)3-(-2)=     By the Mean Value Theorem, we know there exists a cc in the open interval (−2,3)(-2,3) such that f'(c)f′(c) is equal to this mean slope. For this problem, there is only one cc that works. Find it.    

Question 7. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=2x3−9x2−24x+3f(x)=2x3-9x2-24x+3 on the interval [−5,7][-5,7]. Find the average or mean slope of the function on this interval.     By the Mean Value Theorem, we know there exists a cc in the open interval (−5,7)(-5,7) such that f'(c)f′(c) is equal to this mean slope. For this problem, there are two values of cc that work. The smaller one is     and the larger one is    

Question 8. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=1xf(x)=1x on the interval [4,8][4,8]. Find the average or mean slope of the function on this interval.     By the Mean Value Theorem, we know there exists a cc in the open interval (4,8)(4,8) such that f'(c)f′(c) is equal to this mean slope. For this problem, there is only one cc that works. Find it.    

Question 9. Last Attempt:  0 out of 1 Score in Gradebook:   0 out of 1

Consider the function f(x)=8√x+2f(x)=8x+2 on the interval [1,8][1,8]. Find the average or mean slope of the function on this interval.     By the Mean Value Theorem, we know there exists a cc in the open interval (1,8)(1,8) such that f'(c)f′(c) is equal to this mean slope. For this problem, there is only one cc that works. Find it.  

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