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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.
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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|
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OpenStudy (misty1212):
that tells you that there is a local maximum at \(x=0\) as in the picture
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