Another Calculus problem

[sdaccord01]

Hi,

I have another Calculus problem that I'm having difficulty solving.

Here's the problem:
f(x) = { cx + d for x <= 2
{ x^2 - cx for x > 2

f is differentiable at x = 2

What is c + d?

The answer is -2, but I'm not too sure how this problem is solved. Thanks in advance!

 

[Raghu]

f(x) is continuous at 2.
f(x-) = f(x+) = f(x), at x=2

f(x) is differentiable at 2.
f'(x-) = f'(x+), at x=2

2 equations, 2 variables. Solve for c, d. Find c+d.

 

[Leros]

Since you know its differentiable at x= 2, you know that both equations have the same value at x=2. You also know that both equations have the same slope at x=2.

 

[sdaccord01]

Makes sense, thanks for your help!