Question

Is this statment true? Please explain.

At a relative extrema, f'(x) = 0

Answer 1

The statement is true, because f'(x) deals with the slope of a tangent line. At any extrema (maximum or minimum point), the tangent line will be horizontal, meaning that it has a slope of 0. Since f'(x) is the slope of the tangent line, we can say that f'(x)=0 at the extrema.