Explain why a differentiable function whose derivative satisfies for every cannot…

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Explain why a differentiable function

f:\mathbb R\to\mathbb R

whose derivative satisfies

f'(x)>0

for every

x\in\mathbb R

cannot possess a local maximum or a local minimum anywhere on

\mathbb R

. Your explanation should clearly connect the sign of the derivative with the behaviour of the function.