Question

Find a and b such that f is differentiable everywhere.

f(x)={(cos(x), x<0), (ax+b, x >=0)}

I'm pretty much lost right now.

Answer 1

Here's the question formatted better.

Answer 2

I've done some work on the limits approaching 0 from the left and right, but I'm getting a as undefined and I don't think that's correct.

Answer 3

So not only do you want the functions to match at x=0 but you want the derivatives of the functions to match up at x=0.

Answer 4

Right

Answer 5

Show me what your work looks like and I'll find where you need fixing

Answer 6

So the derivative of cos(x) is -sin(x), and the derivative of ax+b is a

Answer 7

Awesome, ok good, now what?

Answer 8

err

Answer 9

a needs to equal -sin(x)

Answer 10

so a = 0?

Answer 11

@Kainui

Answer 12

Yeah, exactly.