Practice problems/A photographer at the skatepark

Figure 1. The shape of the half-pipe, $h(x)$, with camera at height $c$.

A photographer is taking pictures at a skatepark. The "half-pipe" has the shape of a function given by $$h(x)=x^3-6x^2+11x-6$$ where $x$ is the horizontal distance from the photographer and $h(x)$ is the height of the half-pipe surface above the point $x$ (see Figure 1), both measured in tens of meters. The photographer has his camera mounted on a tall rod. He would like to hold the camera at a height $c$ that is high enough so that there is no part of the half-pipe hidden from view. What is the minimum value of $c$ for which this will be the case?

[This problem is a bit tricky.]