Calc

Suppose that f'(c)=0, f''(c)=0 and f'''(c)>0 . What, if anything, happens to the graph of the function f at x = c? Explain clearly and completely.

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asked by Ashley
  1. the slope has a minimum at x=c.

    f"(c)=0 means it's an inflection point.

    Think of the graph f(x) = x^3

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    posted by Steve
  2. So is it just an inflection point?

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    posted by Ashley
  3. yes. The f"' nonzero makes sure that it's not just a cup like x^4.

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    posted by Steve

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