Consider $\displaystyle f(x) = asinhx + bcoshx$ where a and b are real numbers.

For what values of a and b does f have an extremum at x = 0?

For what values of a and b does f have an extremum at x = c?

I started out by differentiating:

$\displaystyle f'(x) = acoshx + bsinhx$

At extremum f'(x) = 0. So setting f'(x) = 0 and x = 0,

$\displaystyle 0 = a*1 + b*0 $

? Doesn't seem to be correct.

I don't know where to go from here to solve this problem. If anyone could help me out, would be greatly appreciated, I don't understand the overall concept of hyperbolic functions very well. Thanks!