Chapter 3: Q. 32 (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.
$f (x) = 3^{x} - 2^{x}$

Short Answer

Expert verified

The critical points are $x = \frac{\ln (\ln (2)) - \ln (\ln (3))}{\ln (3) - \ln (2)}$ . The graph of the function is shown below .

Step by step solution

Step 1. Given information .

Consider the given function $f (x) = 3^{x} - 2^{x}$ .

Step 2. Find the critical points .

The critical points are the points where the function is defined and its derivative is zero or undefined .

Differentiate the given function .

$f (x) = 3^{x} - 2^{x} f' (x) = \frac{\ln (\ln (2)) - \ln (\ln (3))}{\ln (3) - \ln (2)}$

Therefore the critical point is $x = \frac{\ln (\ln (2)) - \ln (\ln (3))}{\ln (3) - \ln (2)}$ .

Step 3. Plot the graph .

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

From the above graph the function f has local maximum because the turning point is on 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.
$f (x) = 3^{x} - 2^{x}$

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=3x-2x

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

Calculus

Theoretical and Mathematical Physics

Geometry

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Pure Maths

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.
$f (x) = 3^{x} - 2^{x}$