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exam_2_review.pdf
MATH 115 EXAM 2 Review
Name & Class Time:
Answer the questions in the spaces provided. There are 14 questions for a total of 90 points.
You are expected to do your own work. SHOW ALL WORK.
1. (5 points) Differentiate f(x) = −15 x3
. Which of the following is f ′(x)?
A. −45 x2
B. 0 C. 45
x4 D. none of the above.
2. (5 points) Differentiate g(x) = 4 3 √ x + 5
√ x. Which of the following is g′(x)?
A. 12 −3 √ x + 5 1
√ x B.
4
3 3 √ x2
+ 5
2 √ x
C. 4
3 √ x2
+ 5 √ x
D. none of the above.
MATH 115 Exam-2
3. (5 points) Differentiate g(x) = 3x− 4 x2
. Which of the following is g′(x)?
A. 3
2x B.
(x2)(3) − (3x− 4)(2x) x4
C. (3x− 4)(2x) − (x2)(3)
x4 D. none of the
above.
4. (5 points) Differentiate h(x) = (x5 − 4x3 + x)5. Which of the following is h′(x)? A. 5(x5 − 4x3 + x)4(5x4 − 12x2 + 1) B. 5(5x4 − 12x2 + 1)4 C. 5(5x4 − 12x2 + 1)4(x5 − 4x3 + x) D. none of the above.
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MATH 115 Exam-2
5. (5 points) Differentiate f(x) = (x + 3)7(7 −x)5?
6. (5 points) Differentiate g(x) = 4 3 √ x + 5
√ x.
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MATH 115 Exam-2
7. (5 points) Differentiate f(x) = x √ x2 + 5 to find f ′(x)?
8. (5 points) Differentiate g(x) = x2 + 3x + 1
2x3 + 3 .
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MATH 115 Exam-2
9. (5 points) Differentiate f(x) = (g(x))3(h(x))4
(q(x))3 .
10. (5 points) Differentiate g(x) = 10x3
(1 + 5x)4 .
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MATH 115 Exam-2
11. (10 points) Find an equation of the tangent line to the graph of y = x + (4/x) at the point (4,5).
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MATH 115 Exam-2
12. (10 points) Find points on the graph of f(x) = x3 − 3x2 where the tangent line is horizontal, i.e. where the slope m = 0.
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MATH 115 Exam-2
13. (10 points) For the function f given, find the desired information.
(a) Find the critical values.
(b) Find the intervals in which f(x) is increasing.
(c) Find the intervals in which f(x) is decreasing.
(d) Find the intervals in which f(x) is concave up.
(e) Find the intervals in which f(x) is concave down.
(f) Two inflection points of f(x) are, the smaller one is x = and the other is x = .
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MATH 115 Exam-2
14. (10 points) Determine which function is the derivative of the other?
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