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

Answer 1

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

Answer 2

Huh...?

Answer 3

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

Answer 4

m = anything
b = anything

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

Answer 5

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

Answer 6

4=2m+b

Answer 7

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

Answer 8

SO m=4

Answer 9

4=2(4)+b

Answer 10

b= -4

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

Nvm, I understand it now :D Thanks