At what point does the curve have maximum curvature? y = 3e^x

Solution:

Given a curve modeled by the function y = 3e^x

A function to have maximum, its double derivative should be negative

y’ = 3e^x {since derivative of e^x is e^x}

y’’ = 3e^x < 0

Divide by 3

e^x < 0

x < ln(0)

Therefore, for all x less than ln(0), the given curve has maximum curvature.

At what point does the curve have maximum curvature? y = 3e^x

Summary:

At x < ln(0) point, does the curve have maximum curvature; y = 3e^x.