A function f(x) is defined to equal cos(ax) + b for x>=0 and 2 – x3 for x < 0, where a and b are constants. It is known that this function is differentiable everywhere. Find all possible values of a and b
I posted this quesiton earlier, and I performed the steps as you indicated, ie lim x-->0+ f'(x) = lim x-->0- f'(x), so
lim x-->0- f'(x) = -3x^2 = lim x-->0+f'(x) = -asin(ax), and after some more math, I ended up with 0 = 0, which I concluded that a could be anything. I know theere is something wrong. This is why I posted this question.