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Let
h(x)=-2x^(3)-7.
The absolute maximum value of
h over the closed interval
[-3,2] occurs at what
x-value?
Choose 1 answer:
(A) -3
(B) 2
(C) 1
(D) -2

Let $h(x)=-2 x^{3}-7$ . $\newline$ The absolute maximum value of $h$ over the closed interval $[-3,2]$ occurs at what $x$ -value? $\newline$ Choose $1$ answer: $\newline$ (A) $-3$ $\newline$ (B) $2$ $\newline$ (C) $1$ $\newline$ (D) $-2$

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Full solution

Q. Let

h(x)=-2 x^{3}-7

.

\newline

The absolute maximum value of

h

over the closed interval

[-3,2]

occurs at what

x

-value?

\newline

Choose

1

answer:

\newline

(A)

-3

\newline

(B)

2

\newline

(C)

1

\newline

(D)

-2

Find Derivative: To find the absolute maximum value of the function $h(x)$ on the closed interval $[-3,2]$ , we need to evaluate the function at the critical points and the endpoints of the interval. The critical points are where the derivative $h'(x)$ is zero or undefined.
Find Critical Points: First, we find the derivative of $h(x)$ . The derivative of $h(x)=-2x^3-7$ with respect to $x$ is $h'(x)=-6x^2$ .
Evaluate Function: Next, we set the derivative equal to zero to find the critical points: $-6x^2 = 0$ . Solving for $x$ gives us $x = 0$ as the only critical point within the interval $[-3,2]$ .
Evaluate at $-3$ : Now we evaluate the function $h(x)$ at the critical point and the endpoints of the interval. We have three points to consider: $x = -3$ , $x = 0$ , and $x = 2$ .
Evaluate at $0$ : Evaluating $h(x)$ at $x = -3$ : $h(-3) = -2(-3)^3 - 7 = -2(-27) - 7 = 54 - 7 = 47$ .
Evaluate at $2$ : Evaluating $h(x)$ at $x = 0$ : $h(0) = -2(0)^3 - 7 = -7$ .
Compare Values: Evaluating $h(x)$ at $x = 2$ : $h(2) = -2(2)^3 - 7 = -2(8) - 7 = -16 - 7 = -23$ .
Maximum Value: Comparing the values of $h(x)$ at $x = -3$ , $x = 0$ , and $x = 2$ , we find that the maximum value is $47$ , which occurs at $x = -3$ .

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h(x)=-2 x^{3}-7

\newline

The absolute maximum value of

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The absolute maximum value of

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\newline

4

\newline

5

\newline

6

\newline

7

\newline

What is the probability of picking a number greater than

5

and then picking a

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\newline

Write your answer as a percentage.

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