for which value of x

Question

The graph of f is shown in the figure.

(a)For which values of x is f '(x) zero? (Enter your answers as a comma-separated list.)

x = 

 

For which values of x is f '(x) positive? (Enter your answer using interval notation.)

 

For which values of x is f '(x) negative? (Enter your answer using interval notation.)

 

What do these values mean?

f is  ---Select--- increasing decreasing when f ' > 0

 and f is  ---Select--- increasing decreasing when f ' < 0.

(b)For which values of x is f ''(x) zero? (Enter your answers as a comma-separated list.)

x = 

 

For which values of x is f ''(x) positive? (Enter your answer using interval notation.)

 

For which values of x is f ''(x) negative? (Enter your answer using interval notation.)

 

What do these values mean?

f is  ---Select--- concave up concave down when f '' > 0

 and f is  ---Select--- concave up concave down when f '' < 0.

Answer 1

(a) x=2, -2

(b) (-infinity,2) U (2,infinity)

(c) (-2,2)

f is increasing when f'>0

f is decreasing when f'<0

f'' is zero at x=0 is a safe bet