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Math Help - derivative proof

  1. #1
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    derivative proof

    show that if the second derivative of function f is greated than zero in the interval [a,b] then the first derivative of function f has atmost one zero in[a,b].and what iff the second derivative of function f is less than 0 throughout [a,b] instead

    in the proof do we have to generalise the ppolynomial or do directly by graph

    please help
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  2. #2
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    Re: derivative proof

    If the derivative of a function is greater than zero, then it is an increasing function, so it can cross the x-axis at most once. In this case, the function is f'(x).

    - Hollywood
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