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.]