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

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. 

1 Answer

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  • 5 days ago

    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.

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