Assume $f(x)$ is differentiable at $e$. Prove that if $f\,'(x)\lt 0$, then $f(e-k)\gt f(e)\gt f(e+k)$ for all positive $k$ sufficiently small.
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Lesson Parent:
Problem:
Assume $f(x)$ is differentiable at $e$. Prove that if $f\,'(x)\lt 0$, then $f(e-k)\gt f(e)\gt f(e+k)$ for all positive $k$ below some sufficiently small value.
Answer:
It is true that if $f\,'(x)\lt 0$, then $f(e-k)\gt f(e)\gt f(e+k)$ for all positive $k$ below some sufficiently small value.
