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3. A function h is differentiable with h'(x) everywhere except x = 2 where h has a vertical asymptote. Find all critical numbers of h and classify each as a local maximum, local minimum, or neither. (x+4)(x − 1)² x-2 =

3. A function h is differentiable with h'(x) everywhere except x = 2 where h has a vertical asymptote. Find all critical numbers of h and classify each as a local maximum, local minimum, or neither. (x+4)(x − 1)² x-2 =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(x+4)(x − 1)² x - 2 = 3. A function h is differentiable with h'(x) everywhere except x 2 where h has a vertical asymptote. Find all critical numbers of h and classify each as a local maximum, local minimum, or neither. =
Transcribed Image Text:(x+4)(x − 1)² x - 2 = 3. A function h is differentiable with h'(x) everywhere except x 2 where h has a vertical asymptote. Find all critical numbers of h and classify each as a local maximum, local minimum, or neither. =
Expert Solution
Step 1

Given:

The function h is differentiable with h'x=x+4x-12x-2 everywhere except x=2 where h has a vertical asymptote.

Vertical Asymptote:

To find the vertical asymptote, set x-2=0.

Then, the vertical asymptote of h is x=2.

Critical Numbers:

Collect all the elements c in the domain of the function f such that f'x=0 or f'x is undefined.

 

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