f(x) = { x^2; x 2 Find the values of m and b that make the function differentiable and continuous everywhere

Question

f(x) = { x^2; x<=2
          { mx+b; x> 2 
Find the values of m and b that make the function differentiable and continuous everywhere

agreene · Answer

Since mx+b is a linear function,  $$ m= \mathbb{R},b= \mathbb{R}$$

anonymous · Answer

Huh...?

anonymous · Answer

Am I supposed to set the 2 equations equal to each other?
(2)^2=2m+b

agreene · Answer

m = anything
b = anything

You cant put any constants in there to make them not continuous because it is a linear equation.

anonymous · Answer

But there is an answer... not just 'anything'... except I do not know how to get it.

anonymous · Answer

4=2m+b

anonymous · Answer

at x=2, dy/dx= 2x = 4

anonymous · Answer

SO m=4

anonymous · Answer

4=2(4)+b

anonymous · Answer

b= -4

anonymous · Answer

You are finding the derivative of 4=2m+b?

anonymous · Answer

no, the deriv ative of y=x^2, and equating it to the gradient of the line.

anonymous · Answer

Why are you setting the derivative of y=x^2 = 4?

anonymous · Answer

Nvm, I understand it now :D Thanks