answersLogoWhite

0

Log x is defined only for x > 0.

The first derivative of log x is 1/x, which, for x > 0 is also > 0

The second derivative of log x = -1/x2 is always negative over the valid domain for x.

Together, these derivatives show that log x is a strictly monotonic increasing function of x and that its rate of increase is always decreasing. Consequently log x is convex.

User Avatar

Wiki User

13y ago

Still curious? Ask our experts.

Chat with our AI personalities

CoachCoach
Success isn't just about winning—it's about vision, patience, and playing the long game.
Chat with Coach
JudyJudy
Simplicity is my specialty.
Chat with Judy
RafaRafa
There's no fun in playing it safe. Why not try something a little unhinged?
Chat with Rafa

Add your answer:

Earn +20 pts
Q: How do you show log x is convex?
Write your answer...
Submit
Still have questions?
magnify glass
imp