# Exercise 12.4.4

Show that the function $f(x) = 2^x$ is convex.

Like $f'(x) = 2^x \ln{2}$ and $f''(x) = 2^x \ln^2 2$ which is positive for all real numbers, thus the function is convex.

The again, the Instructor Manual solves this without calculus. Key point: learn calculus.