The polynomial function $h$ is defined by $h(x)=-x^{3}+5 x^{2}-4 x-4$.
Use the ALEKS graphing calculator to find all the points $(x, h(x))$ where there is a local minimum.
Round to the nearest hundredth.
If there is more than one point, enter them using the "and" button.

Step 1 ：Define the polynomial function \(h(x) = -x^{3} + 5x^{2} - 4x - 4\).

Step 2 ：Find the derivative of the function \(h'(x) = -3x^{2} + 10x - 4\).

Step 3 ：Set the derivative equal to zero and solve for \(x\) to find the critical points. The solutions are \(x = \frac{5}{3} - \frac{\sqrt{13}}{3}\) and \(x = \frac{\sqrt{13}}{3} + \frac{5}{3}\).

Step 4 ：Substitute these x-values back into the original function to find the corresponding y-values. The points are \(\left(\frac{5}{3} - \frac{\sqrt{13}}{3}, -\frac{32}{3} - \left(\frac{5}{3} - \frac{\sqrt{13}}{3}\right)^{3} + 5\left(\frac{5}{3} - \frac{\sqrt{13}}{3}\right)^{2} + 4\frac{\sqrt{13}}{3}\right)\) and \(\left(\frac{\sqrt{13}}{3} + \frac{5}{3}, -\left(\frac{\sqrt{13}}{3} + \frac{5}{3}\right)^{3} - \frac{32}{3} - 4\frac{\sqrt{13}}{3} + 5\left(\frac{\sqrt{13}}{3} + \frac{5}{3}\right)^{2}\right)\).

Step 5 ：Identify the local minimum from these points. The local minimum is \(\left(\frac{5}{3} - \frac{\sqrt{13}}{3}, -\frac{32}{3} - \left(\frac{5}{3} - \frac{\sqrt{13}}{3}\right)^{3} + 5\left(\frac{5}{3} - \frac{\sqrt{13}}{3}\right)^{2} + 4\frac{\sqrt{13}}{3}\right)\).

Step 6 ：Round the local minimum to the nearest hundredth. The final answer is \(\boxed{(0.54, -5.18)}\).