Please Help! Find the second derivative of f(x) = x3 + x4 and its sign chart. Which of the following is not true about f?

Question

Find the second derivative of  f(x) = x^3 + x^4 and its sign chart. Which of the following is not true about f? I know the second derivative is 12x^2+6x but i am a little confused because it asks about f not f'.

A) f is concave down on (-1/2, 0)

B) f is concave up on (-∞, -1/2) U (0, ∞)

C) f is concave up on (-1/2, 0)

D) f has inflection points at x=-1/2 and x= 0.

E) All are not true.

az_lender · Answer

I agree that f"(x) = 12x^2 + 6x.
This expression will be 0 when x is 0 or -1/2.
So on (0,infinity) f is concave up; on (-1/2,0) it's concave down; on (-infinity,-1/2) concave up.

A is true.
B is true.
C is false.
D is true.
E is false.

Please Help! Find the second derivative of f(x) = x3 + x4 and its sign chart. Which of the following is not true about f?

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