find the values of c that make the following function continuous everywhere for 2x^2 + c if x

Question

find the values of c that make the following function continuous everywhere for 2x^2 + c if x<2 and cx^2+2 if x <2

agent0smith · Answer

The endpoints of the lines must meet - 

ie when x=2, 
$$\Large 2x^2 + c = cx^2+2$$

anonymous · Answer

so would you then write it out 8+c=c(4)+2? or where would you go once you know you have to set them equal?

agent0smith · Answer

That's right. Now find c from that.

anonymous · Answer

does it just come out to be c=2?

agent0smith · Answer

Yep. Which if you think about it, you can see it's 2 from here:

$$\Large 2x^2 +c = cx^2 +2 $$

from  here, the 'x' parts must be equal, and so must the number parts...

ie 2x^2 = cx^2 (ie c has to be 2) and c = 2