APPLIED CALCULUS FOR LIFE SCI
abdullah777
homework23.pdf
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Student: _____________________ Date: _____________________
Instructor: Edward Tawiah Course: Applied Calc
Assignment: hw 2 & 3
Differentiate.
F(x) = (7x + 3) 2
(x)F =
Use the product rule to find the derivative of the following.
p(y) = y + y 8y − 9y − 1 − 2 − 3 − 4
(y)p =
For the function below, find a) the critical numbers; b) the open intervals where the function is increasing; and c) the open intervals where it is decreasing.
f(x) = x + 5
x + 2
a) Find the critical number(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The critical number(s) is/are .
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There are no critical numbers.
b) Determine the interval(s) on which the function is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. List any interval(s) on which the function is increasing.
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B. The function is never increasing.
c) Determine the interval(s) on which the function is decreasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. List any interval(s) on which the function is decreasing.
.
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B. The function is never decreasing.
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For the following function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where the function is decreasing.
f(x) = − 3 + x
2
5
a. Find the critical numbers. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The critical number(s) is/are .
(Simplify your answer. Use a comma to separate answers as needed.)
B. There are no critical numbers for this function.
b. Find the open intervals where the function is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The function is never increasing.
B. The function is increasing on the open interval(s) .
(Type your answer in interval notation. Use a comma to separate answers as needed.)
c. Find the open intervals where the function is decreasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The function is decreasing on the open interval(s) .
(Type your answer in interval notation. Use a comma to separate answers as needed.)
B. The function is never decreasing.
Find the derivative of the function.
y = 7
x 5
− 9
x
dy
dx =
Find the derivative of the function.
q( )y = 6y y + 32 2
7
6
(y)q =
Find the derivative of the function.
y = 3 3x + 1
dy
dx =
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Find the derivative of the function.
y = 5 2x 2
dy
dx =
For the function below, find a) the critical numbers; b) the open intervals where the function is increasing; and c) the open intervals where it is decreasing.
f(x) = 2.5 + 4.6x − 1.3x 2
a) The critical number(s) is/are .
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
b) List any interval(s) on which the function is increasing.
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
c) List any interval(s) on which the function is decreasing.
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
For the function below, find a) the critical numbers; b) the open intervals where the function is increasing; and c) the open intervals where it is decreasing.
f(x) = 12x − 81x − 324x + 8 3 2
a) Find the critical number(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The critical number(s) is/are .
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There are no critical numbers.
b) List any interval(s) on which the function is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The function is increasing on the interval(s) .
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B. The function is never increasing.
c) List any interval(s) on which the function is decreasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. .
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B. The function is never decreasing.
The function is decreasing on the interval(s)
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Determine all relative extrema for the following function.
f(x) = 2x − 256
x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. Relative extrema at x =
(Use a comma to separate answers as needed.)
B. No relative extrema
Find the x-values of all points where the function defined as follows has any relative extrema. Find the values of any relative extrema.
f(x) = 8x + ln x
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choices.
A. There is a relative minimum of at x .=
B. There is a relative maximum of at x .
C. There is a relative minimum of at x . There is a relative
maximum of
=
at x = .
D. There are no relative extrema.
For the function f(x) , find f (x), the third derivative of f, and f (x), the fourth derivative of f.= 3x − 4x + 3x + 5x + 5 5 4 3 2 (4)
f (x) =
f (x)(4) =
Find the open intervals where the function f(x) is concave upward or concave downward. Find any inflection points.
= − 3x + 27x + 171x − 4 3 2
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The function has a point of inflection at .
(Type an ordered pair. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.)
B. The function does not have an inflection point.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The function is concave upward on the interval(s) .
(Type your answer in interval notation. Use a comma to separate answers as needed.)
B. The function is never concave upward.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The function is concave downward on the interval(s) .
(Type your answer in interval notation. Use a comma to separate answers as needed.)
B. The function is never concave downward.
=
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Assume that the number of bacteria R(t) (in millions) present in a certain culture at time t (in hours) is given by R(t) = t (t − 15 2
a. At what time before hours will the population be maximized?8 b. Find the maximum population.
a. The population will be maximized at t hours.=
b. The maximum population is million bacteria.
When an object is dropped straight down, the distance (in feet) that it travels in t seconds is given by s(t) .= − 16t 2
Find the velocity at each of the following times. a. After seconds.2 b. After seconds.6 c. After seconds.9 d. Find the acceleration.
a. The velocity after seconds is ft/sec.2
b. The velocity after seconds is ft/sec.6
c. The velocity after seconds is ft/sec.9
d. The acceleration is .ft sec 2
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