12.4 Exercise 164

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 $x = 1.$