Chapter 3: Q. 30 (page 248)

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.
$f (x) = {(2 x - 1)}^{5}$

Short Answer

Expert verified

The critical point is $x = \frac{1}{2}$ . The graph of the function is shown below .

Step by step solution

Step 1. Given information .

Consider the given function $f (x) = {(2 x - 1)}^{5}$ .

Step 2. Find the critical points .

To find the critical points differentiate the given function .

$f (x) = {(2 x - 1)}^{5} f' (x) = 5 {(2 x - 1)}^{4} = 5 {(2 x - 1)}^{2} {(2 x - 1)}^{2}$

Further simplify .

Put $f' (x) = 0$

${(2 x - 1)}^{2} {(2 x - 1)}^{2} = 0 x = \frac{1}{2}, x = \frac{1}{2}$

Therefore the critical point is $x = \frac{1}{2}$ .

Step 3. Plot the graph .

The graph of the given function by using graphing utility is shown below.

From the given graph function f has local maximum because the turning point is on the positive axis .

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Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.
$f (x) = {(2 x - 1)}^{5}$

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Find the critical points .

Step 3. Plot the graph .

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Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.fx=2x-15

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Find the critical points .

Step 3. Plot the graph .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Study anywhere. Anytime. Across all devices.

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.
$f (x) = {(2 x - 1)}^{5}$