Problems
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- Where on the x-axis is $f(x)=x^4-4x^3$ increasing or decreasing?
- Where on the x-axis is $f(x)=1/(x+1)$ increasing or decreasing?
- 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.
- Assume $f(x)$ is differentiable at $e$. Prove that if $f\,'(x)\gt 0$, then $f(e-k)\lt f(e)\lt f(e+k)$ for all positive $k$ sufficiently small.
- Prove Theorem 2 in the lesson 'Geometry of Functions IV: Using Derivatives To Identify Increasing and Decreasing Functions'.
- Prove Theorem 1 in the lesson 'Geometry of Functions IV: Using Derivatives To Identify Increasing and Decreasing Functions'.
