Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose $f'(x)$ is a differentiable and increasing function for all $x$. Which number is the largest and why? $f(4+\Delta x)$ or $f(4)+f'(4)\Delta x$?

I believe $f(x)$ must be concave up everywhere since the derivative is increasing, but I am not sure how to figure out which of those is larger based on that. Would the tangent like approximation be $f(4+\Delta x)$ or $f(4)+f'(4)\Delta x$?

Thank you!

share|cite|improve this question
up vote 0 down vote accepted

The tangent line approximation at $x=4$ is $f(4)+f'(4)(x-4)$. You probably mean $x-4$ by $\Delta x$. It cannot be $f(4+\Delta x)$ as this can not be linear-a straight line does not have increasing derivative.

You are right that $f(x)$ is concave up everywhere. Does that mean it is above or below the tangent line?

share|cite|improve this answer
if its concave up then this would mean that f(x) is above the tangent line, so would this would make the tangent line approximation less I do believe? – user59714 Feb 13 '13 at 23:47
@user59714: that is correct. – Ross Millikan Feb 14 '13 at 0:03
thanks a bunch! :) – user59714 Feb 14 '13 at 0:04

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.