Question

Medal to first person!

Suppose that y=f(x) = sqrt(2x), x>=0

Find a c > 0 such that the tangent line to the curve y = f(x) at x = c has the same slope as the tangent line to the curve y = f^–1(x) at x = c.

You get:

c = 1/8

c = 1/2

c = (1/8)^(1/3)

c = (1/3)^(2/3)

c = (1/2)^(1/3)

Answer 1

Its 1/2^(1/3)