Math / Calculus

QuestionFor $f(x)$ in the figure below, find the $x$ -values of the global maximum and global minimum on the domain $-10 \leq x \leq 5$ .
\begin{array}{c} \includegraphics[scale=0.5]{graph.png} \\ \text{50} \\ \text{150} \\ \text{100} \\ f(x) \\ x \\ -15 \quad -10 \quad -5 \quad 5 \quad 10 \quad 15 \quad 20 \\ \end{array}

Studdy Solution

STEP 1

1. The function $f(x)$ is continuous over the domain $-10 \leq x \leq 5$ .
2. The graph of $f(x)$ is provided, and we can visually identify maxima and minima.
3. We are looking for the global maximum and minimum $x$ -values within the specified domain.

STEP 2

1. Identify critical points and endpoints within the domain.
2. Evaluate $f(x)$ at these points to determine the global maximum and minimum.
3. Conclude the $x$ -values for the global maximum and minimum.

STEP 3

Examine the graph to identify any critical points within the domain $-10 \leq x \leq 5$ . These are points where the slope is zero or undefined (peaks, troughs).

STEP 4

Identify the endpoints of the domain, which are $x = -10$ and $x = 5$ .

STEP 5

Evaluate $f(x)$ at the critical points and endpoints identified in Step 1. Compare these values to find the highest and lowest values.

STEP 6

From visual inspection of the graph: - Assume $x = a$ is the $x$ -value of the peak within the domain. - Assume $x = b$ is the $x$ -value of the trough within the domain. - Evaluate $f(a)$ , $f(b)$ , $f(-10)$ , and $f(5)$ .

STEP 7

Determine the $x$ -value corresponding to the highest $f(x)$ value for the global maximum.

STEP 8

Determine the $x$ -value corresponding to the lowest $f(x)$ value for the global minimum.
The $x$ -value of the global maximum is $x = a$ , and the $x$ -value of the global minimum is $x = b$ .

Was this helpful?

Studdy Solution

STEP 1

1. The function $f(x)$ is continuous over the domain $-10 \leq x \leq 5$ .
2. The graph of $f(x)$ is provided, and we can visually identify maxima and minima.
3. We are looking for the global maximum and minimum $x$ -values within the specified domain.

STEP 2

1. Identify critical points and endpoints within the domain.
2. Evaluate $f(x)$ at these points to determine the global maximum and minimum.
3. Conclude the $x$ -values for the global maximum and minimum.

STEP 3

Examine the graph to identify any critical points within the domain $-10 \leq x \leq 5$ . These are points where the slope is zero or undefined (peaks, troughs).

STEP 4

Identify the endpoints of the domain, which are $x = -10$ and $x = 5$ .

STEP 5

Evaluate $f(x)$ at the critical points and endpoints identified in Step 1. Compare these values to find the highest and lowest values.

STEP 6

From visual inspection of the graph: - Assume $x = a$ is the $x$ -value of the peak within the domain. - Assume $x = b$ is the $x$ -value of the trough within the domain. - Evaluate $f(a)$ , $f(b)$ , $f(-10)$ , and $f(5)$ .

STEP 7

Determine the $x$ -value corresponding to the highest $f(x)$ value for the global maximum.

STEP 8

Determine the $x$ -value corresponding to the lowest $f(x)$ value for the global minimum.
The $x$ -value of the global maximum is $x = a$ , and the $x$ -value of the global minimum is $x = b$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

1. The function f(x) f(x) f(x) is continuous over the domain −10≤x≤5-10 \leq x \leq 5−10≤x≤5.2. The graph of f(x) f(x) f(x) is provided, and we can visually identify maxima and minima.3. We are looking for the global maximum and minimum x x x-values within the specified domain.

STEP 2

1. Identify critical points and endpoints within the domain.2. Evaluate f(x) f(x) f(x) at these points to determine the global maximum and minimum.3. Conclude the x x x-values for the global maximum and minimum.

STEP 3

Examine the graph to identify any critical points within the domain −10≤x≤5-10 \leq x \leq 5−10≤x≤5. These are points where the slope is zero or undefined (peaks, troughs).

STEP 4

Identify the endpoints of the domain, which are x=−10 x = -10 x=−10 and x=5 x = 5 x=5.

STEP 5

Evaluate f(x) f(x) f(x) at the critical points and endpoints identified in Step 1. Compare these values to find the highest and lowest values.

STEP 6

From visual inspection of the graph: - Assume x=a x = a x=a is the x x x-value of the peak within the domain. - Assume x=b x = b x=b is the x x x-value of the trough within the domain. - Evaluate f(a) f(a) f(a), f(b) f(b) f(b), f(−10) f(-10) f(−10), and f(5) f(5) f(5).

STEP 7

Determine the x x x-value corresponding to the highest f(x) f(x) f(x) value for the global maximum.

STEP 8

Determine the x x x-value corresponding to the lowest f(x) f(x) f(x) value for the global minimum. The x x x-value of the global maximum is x=a x = a x=a, and the x x x-value of the global minimum is x=b x = b x=b.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The function $f(x)$ is continuous over the domain $-10 \leq x \leq 5$ .
2. The graph of $f(x)$ is provided, and we can visually identify maxima and minima.
3. We are looking for the global maximum and minimum $x$ -values within the specified domain.

1. Identify critical points and endpoints within the domain.
2. Evaluate $f(x)$ at these points to determine the global maximum and minimum.
3. Conclude the $x$ -values for the global maximum and minimum.

Examine the graph to identify any critical points within the domain $-10 \leq x \leq 5$ . These are points where the slope is zero or undefined (peaks, troughs).

Identify the endpoints of the domain, which are $x = -10$ and $x = 5$ .

Evaluate $f(x)$ at the critical points and endpoints identified in Step 1. Compare these values to find the highest and lowest values.

From visual inspection of the graph: - Assume $x = a$ is the $x$ -value of the peak within the domain. - Assume $x = b$ is the $x$ -value of the trough within the domain. - Evaluate $f(a)$ , $f(b)$ , $f(-10)$ , and $f(5)$ .

Determine the $x$ -value corresponding to the highest $f(x)$ value for the global maximum.

Determine the $x$ -value corresponding to the lowest $f(x)$ value for the global minimum.
The $x$ -value of the global maximum is $x = a$ , and the $x$ -value of the global minimum is $x = b$ .