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Q. 31

Expert-verified
Found in: Page 248

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# 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.$f\left(x\right)=3x-2{e}^{x}$

The critical point is $x=In\left(\frac{3}{2}\right)$ . The graph of the given function is shown below .

See the step by step solution

## Step 1. Given information .

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

## 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 .

$f\left(x\right)=3x-2{e}^{x}\phantom{\rule{0ex}{0ex}}f\text{'}\left(x\right)=3-2{e}^{x}$

Therefore the critical point is $x=In\left(\frac{3}{2}\right)$ .

## Step 3. Plot the graph .

The graph of the given function is shown below .

From the given graph the function f has local minimum because the turning point is on negative axis .