Exam 2: Applications of the Derivative

Find the interval(s) where f is concave down for $f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 3 } - 5 x + 10$

Is this the graph of the function having the following properties? (I) inflection point at x = 3 (II) no relative maximum point (III) asymptote at x = 5

Which of the following graphs could represent a function having the given properties? (I) asymptotes x = 2 and x = -2 (II) f''(x) > 0 for all x (III) f(x) > 0 for all x > 4

Determine the inflection point of $f ( x ) = 2 x ^ { 3 } - 9 x ^ { 2 } + 12 x - 1$ Enter your answer exactly as just an ordered pair of fractions: $\left( \frac { \mathrm { a } } { \mathrm { b } } , \frac { \mathrm { c } } { \mathrm { d } } \right)$

Is this the graph of the function f(x) = $x ^ { 3 }$ + 3 $x ^ { 2 }$ - 45x + 10?

A large rectangular garden is to be enclosed by a fence and divided into 5 regions by 4 parallel fences across the interior of the garden as shown below. Find the values of l and w for which the total area of the garden is as large as possible, assuming that 120 ft of fencing is available.

Compute the maximum profit when the demand function is $p ( x ) = x ^ { 2 } - 3 x + 2$ and the total cost function is $C ( x ) = \frac { 2 x ^ { 3 } } { 3 } - \frac { 1 } { 2 } x ^ { 2 } - 2 x$ Enter just a reduced fraction of form $\frac { a } { b }$ .

Find the x coordinates of all relative extreme points of $f ( x ) = \frac { 2 } { 3 } x ^ { 3 } - 7 x ^ { 2 } + 24 x - 72$

If a function has second derivative f ''(x) = $x ^ { 2 }$ ( $x ^ { 2 }$ - 4) is (0, 0) an inflection point?

A homebuilder's advertisement promises a house with a finished recreation room of 300 square feet. Two perpendicular walls of the room are to be paneled at a cost of $5 per running foot. A third side will be built out of windows at a cost of $10 per running foot. What dimensions should the room have to minimize the homebuilder's cost? Enter your answer as: length of side using cinder, length of other side.

Which of the following graphs could represent a function with the following properties? I. f(x) > 0, for x < 0 II. $f ^ { \prime }$ (x) ? 0, for all x III. $f ^ { \prime }$ (0) = 0

Is this the graph of a function having the following properties? (I) defined for x ≥ -1 (II) horizontal asymptote at y = 3 (III) increasing for all x ≥ -1

Compute the minimal average cost if the total cost function is $C ( x ) = 9 x ^ { 2 } + 5 x + 100$ Enter just an integer.

Compute the maximum product for two positive numbers with the property that the sum of the first plus five times the second is 5000.

Which labeled point has the most negative slope?

Which of the following is (are) true of $f ( x ) = x ^ { 4 } - x ^ { 3 } ?$ (I) (0, 0) is an inflection point (II) $\left( \frac { 1 } { 2 } , - \frac { 1 } { 16 } \right)$ is an inflection point (III) (0, f(0)) is a relative minimum point (IV) f is increasing on (0, 2)

Find the inflection point(s) of $f ( x ) = \frac { x ^ { 3 } } { 3 } - \frac { 5 } { 2 } x ^ { 2 } + 6 x - 36$

Determine the maximum and minimum values of f(x) = 1 - $x ^ { 3 }$ + 3x + 2 on 0 ≤ x ≤ 3 . Enter your answer exactly as: a,b both integers where a is the minimum of f and b is the maximum of f.

Is this the graph of f(x) = $\frac { 1 } { 4 }$ $x ^ { 4 }$ - $x ^ { 3 }$ + 2?

Compute the maximum product for two positive numbers with the property that the sum of the first plus three times the second is 3000.