   Chapter 3.3, Problem 22E

Chapter
Section
Textbook Problem

# 20-27 Sketch the graph of a function that satisfies all of the given conditions.Vertical asymptote x = 0 , f ′ ( x ) > 0   if   x < − 2 , f ′ ( x ) < 0   if   x > − 2   ( x ≠ 0 ) , f ′ ( x ) < 0   if   x < 0 ,     f ′ ′ ( x ) > 0   if   x > 0

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=0,

f'x>0 if x< -2  and f'x<0 if x> -2

f"(x)<0 if x<0 and f "(x)>0 if x

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