Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

Find all values of $a$ and $b$ that make the following function differentiable for all values of $x$: $$ f(x) = \begin{cases} \arctan(ax+b), x<0\\ \pi/4e^{\sin(bx)}, x \geq 0\\ \end{cases} $$

I thought I had this question figured out but it started to get more complicated than I think it should be. Any help would be greatly appreciated, Thank you.

share|cite|improve this question
up vote 1 down vote accepted

It suffices to match the function at 0 and then evaluate the right and left hand limits for the derivatives and match these

$\arctan(b) = \frac{\pi}{4}$ implies that $b = 1$.

$\frac{a}{1+(ax+b)^2} = \frac{a}{1+1} $ set equal to $ \frac{\pi}{4}b =\frac{\pi}{4}$. So $a = \frac{\pi}{2}$

share|cite|improve this answer
Thanks so much, I was definitely over thinking that one – Chance Oct 15 '12 at 5:21

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.