Question

Prove that If f (x) has a local maximum or a local
minimum at x = c, and if f(c) exists, then f(c) = 0

Answer 1

Not true. Consider \(f(x)=x^2+1\) as an example.

Answer 2

Perhaps you meant \(f'(c)=0\) ?

Answer 3

read the statement again its about local maximum and local minimum value of a function not about a simple derivative

Answer 4

I understand the statement. If it is indeed as you've typed it, see my counter-example. At \(x=0\), you have a minimum, yet \(f(0)=1\neq0\).