Applications of Derivatives Review

Question 1

A point of inflection can be found when...

Accepted Answer

f"(x) changes signs

Question 2

Critical numbers for f\left(x\right)=x^4\left(x-3\right)^3

Accepted Answer

0, 3, 12/7

Question 3

Find the inflection point for the function f(x)=x4-x .

Accepted Answer

No point of inflection

Question 4

What is the min length of the segment in quadrant 1 tangent to y=1/x at some point?

Accepted Answer

2\sqrt{2}

Question 5

Find the ANTI-derivative of f'\left(x\right)=\sin\left(x\right)+4x^2

Accepted Answer

-\cos\left(x\right)+\frac{4}{3}x^3+c

Question 6

The function shown here appears to have how many critical points?

Accepted Answer

3

Question 7

The function shown here appears to have how many points of inflection?

Accepted Answer

2

Question 8

Emily sells x bags for $p = 250-0.01x; it costs $c = 100+25x to produce them. Find x to maximize profit.

Accepted Answer

11,250 bags at $137.50

Question 9

SupposeC\left(x\right)=x^3-22x^2+20,000x is the cost to make x cat toys. What x will minimize the AVERAGE cost?

Accepted Answer

11 cat toys

Question 10

Based on the sign chart, which of the following statements is false?

Accepted Answer

f(x) has two critical points

Question 11

The Second Derivative Test...

Accepted Answer

Determines if critical points are local extrema on f(x)

Question 12

Particle on a line has v\left(t\right)=2\sin\left(t\right)-4\cos\left(t\right) and starts at s(0) = 4. Find s(t).

Accepted Answer

-2\cos\left(t\right)-4\sin\left(t\right)+6

Question 13

Find the interval over which the given function is concave up.

Accepted Answer

(1, ∞)

Question 14

Given f(x) =x2 , find the value c on the interval [1, 3] for which the MVT applies.

Accepted Answer

x = 2

Question 15

Find the max area of a rectangle that can be circumscribed about a given rectangle with lenght L = 7 and width W = 4.

Accepted Answer

60.6 square units

Question 16

Based on the sign chart, which of the following statements is false?

Accepted Answer

f(x) has three points of inflection

Question 17

For what c does the curve f\left(x\right)=2x^3+cx^2+10x have max and min points?

Accepted Answer

\left|c\right|>\sqrt{60}

Question 18

What is the constant acceleration required to increase the speed of a car from 20 ft/sec to 45 ft/sec in 5 sec?

Accepted Answer

5 ft/sec2

Question 19

Which of the following is NOT a step when completing an optimization problem.

Accepted Answer

Check for change

Question 20

The First Derivative Test...

Accepted Answer

Determines if critical points are local extrema on f(x)

Question 21

JG estimates taht the marginal cost ($/item) to make space suits is 2.07-.002x. One item is $561. Cost for 100?

Accepted Answer

$755.93

Question 22

Find c that satisfies the MVT for f\left(x\right)=2\sqrt{x} on the interval [4,9]

Accepted Answer

c = 25/4

Question 23

What is a possible ANTI-derivative of f\left(x\right)=12x^3-\sec^2\left(x\right) if f(0) = -3?

Accepted Answer

3x^4-	an\left(xight)-3

Question 24

Given the graph of f'(x), where does f(x) have a minimum?

Accepted Answer

x = 0

Question 25

Find the interval over which the given function is decreasing.

Accepted Answer

(-2, 4)

Applications of Derivatives Review

Questions 25

Applications of Derivatives Review

Questions 25