Given f(x)=4x^2, what is the shortest length from point (32, 1/8) to the given function.

Question

Given f(x)=4x^2, what is the shortest length from point (32, 1/8) to the given function?

Answer 1

The distance is sqrt[(x-32)² + [(4x²-(1/8)]²

The minimum occurs when 2(x-3) + 2[4x²-(1/8)]8x = 0

Collecting terms gives x=1

The distance when x=1 is 30.866