The graph of f ′(x) is continuous and decreasing with an x-intercept at x = 0. Which of the following statements is false?

The graph of f has an inflection point at x = 0.
The graph of f has a relative maximum at x = 0.
The graph of f is always concave down.
The graph of the second derivative is always negative.

Question

The graph of f ′(x) is continuous and decreasing with an x-intercept at x = 0. Which of the following statements is false?

 The graph of f has an inflection point at x = 0.
 The graph of f has a relative maximum at x = 0.
 The graph of f is always concave down.
 The graph of the second derivative is always negative.

misty1212 · Answer

HI!!

anonymous · Answer

Hello!

misty1212 · Answer

the derivative is decreasing and continuous with a zero at $x=0$ means before $x=0$ the derivative is positive, after $x=0$ the derivative is negative

anonymous · Answer

so relative max at x=0 then?

misty1212 · Answer

that means the original function was going up (increasing) then it was going down |dw:1429061449393:dw|

misty1212 · Answer

that tells you that there is a local maximum at $x=0$ as in the picture