MATH SOLVE

2 months ago

Q:
# Find the absolute maximum value of the function

Accepted Solution

A:

The answer to this question is 1. If we differentiate each piece, we get

f'(x) = {2, -2 < x < 0

{ -2x, x>0

The critical number is x = 0. We can also see that f(x) is decreasing on x>0.

We check the end points and critical numbers for the absolute maximum. One end point at

f(-2) = 2(-2) + 1 = -3

The critical number checked gives

f(0) = -0^2 + 1 = 1

The absolute maximum value is 1.

f'(x) = {2, -2 < x < 0

{ -2x, x>0

The critical number is x = 0. We can also see that f(x) is decreasing on x>0.

We check the end points and critical numbers for the absolute maximum. One end point at

f(-2) = 2(-2) + 1 = -3

The critical number checked gives

f(0) = -0^2 + 1 = 1

The absolute maximum value is 1.