Suppose you had a container with a rectangular base whose length runs from $x=a$ to $x=b,$ with a width of one$-$inch. The container has four vertical rectangular sides. You put a piece of igneous rock $($hardened magma$)$ into the container which fits snugly along the bottom and four sides. The top of the piece of rock is irregular and has the equation $y=f(x).$ If the rock were to be heated back to magma and then cooled so that the surface is now flat, how high up the sides would the rock rise? It may be helpful to draw a picture.