Thread: derivative of function

you are asked to find the maximum value of a function. Not having a complete
understanding of the process, you decide to find the derivative of the function, set it
equal to zero, and solve. The resulting value, your reasons, will yield the maximum
point. Explain fully why your method is flawed.

Given finding $\displaystyle f'(x)= 0 \implies x= x_0$ then $\displaystyle f(x_0) \implies \text{max}$