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

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