Find the constant c that makes g continuous on (-infinity, +infinity):

. /

| x^2 - c^2 if x < 4

g(x) = <

| cx + 20 if x >= 4

\

(The dot above doesn't mean anything, but the first line wouldn't line up without a leading character.)

"Continous" just means that the two ends line up, right? So I just have to do:

4

^{2}- c

^{2}= 4c + 20

16 - c

^{2}= 4c + 20

0 = c

^{2}+ 4c + 4

0 = (c + 2)

^{2}

-2 = c

This would make the two ends meet up at (x, y) = (4, 12). Is that okay? I'm not forgetting any "calculus" stuff for this, am I?

Thanks in advance.