Derivatives · Exercise 143

Use the function $f\left(x\right)=x{\left(1-x\right)}^{\frac{2}{5}}$.

Explore the behavior of the graph of $f\left(x\right)$ around $x=1$ by graphing the function on the following domains, [0.9, 1.1], [0.99, 1.01], [0.999, 1.001], and [0.9999, 1.0001]. Use this information to determine whether the function appears to be differentiable at $x=1.$

OpenStax, Precalculus 2e · §12.4 Derivatives · Exercise 143