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Mathematics 72 Online
OpenStudy (anonymous):

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.

OpenStudy (misty1212):

HI!!

OpenStudy (anonymous):

Hello!

OpenStudy (misty1212):

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

OpenStudy (anonymous):

so relative max at x=0 then?

OpenStudy (misty1212):

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

OpenStudy (misty1212):

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

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