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

Answer 1

The endpoints of the lines must meet -

ie when x=2,
\[\Large 2x^2 + c = cx^2+2\]

Answer 2

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?

Answer 3

That's right. Now find c from that.

Answer 4

does it just come out to be c=2?

Answer 5

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