Concavity, Inflection Points and Increasing/Decreasing fun!

Question

I need help with the following:

Suppose that

f(x)=3x^2−16.

(A) List all critical numbers of f. If there are no critical numbers, enter 'NONE'.

Critical numbers = ___0____

(B) Use interval notation to indicate where f(x) is increasing.

Note: Use 'Inf' for ∞, '-Inf' for −∞, and use 'U' for the union symbol.

Increasing:______

(C) Use interval notation to indicate where f(x) is decreasing.

Decreasing:_____

(D)List the x-coordinates of all local maxima of f. If there are no local maxima, enter 'NONE'.

x values of local maxima =______

(E) List the x-coordinates of all local minima of f. If there are no local minima, enter 'NONE'.

x values of local minima =_____

(F) Use interval notation to indicate where f(x) is concave up.

Concave up:_____

(G) Use interval notation to indicate where f(x) is concave down.

Concave down:_____

(H) List the x values all inflection points of f. If there are no inflection points, enter 'NONE'.

Inflection points =____

(I) List all horizontal asymptotes of f. If there are no horizontal asymptotes, enter 'NONE'.

Horizontal asymptotes y=_____0_

(J) List all vertical asymptotes of f. If there are no vertical asymptotes, enter 'NONE'.

Vertical asymptotes x=___4,-4_____

Answer 1

A) f'=6x, x_c=0.y_c=-16

B) f is increasing x>0

C) f is decreasing x<0

D) DNE

E) x_c=0.y_c=-16 local minima

F) f''=6>0 = CCU -inf <x<+inf

G) DNE

H) None

I) None

J) None