Question

What is the maximum vertical distance between the line
y = x + 42
and the parabola
y = x^2 for −6 ≤ x ≤ 7?

Answer 1

looks like this
http://www.wolframalpha.com/input/?i=y%3Dx%2B42%2Cy%3Dx^2+domain+-6..7

Answer 2

so we see that the distance between the parabola and the line is given by
\[x+42-x^2\]
max is at the vertex or at the endpoints of the interval