   Chapter 3.3, Problem 24E

Chapter
Section
Textbook Problem

# 20-27 Sketch the graph of a function that satisfies all of the given conditions. f ′ ( x ) > 0   for all  x ≠ 1 , vertical asymptote x = 1 , f ′ ′ ( x ) > 0   if  x < 1  or  x > 3 , f ′ ′ ( x ) < 0   if   1 < x < 3

To determine

To sketch:

The graph satisfying the given conditions

Explanation

1) Concept:

i. Increasing or Decreasing test:

If f'x>0 then f is increasing

If f'x<0 then f is decreasing

ii. Concavity test:

If f"(x)>0 then the graph of f is concave upward

If f"(x)<0 then the graph of f is concave downward

2) Given:

Vertical asymptote x=1,

f'x>0 for all x1

f"(x)>0 if x<1 or x>3

f"(x)<0 if 1<x<3

3) Calculation:

Vertical asymptote x=1,

f'

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