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:
42 - c2 = 4c + 20
16 - c2 = 4c + 20
0 = c2 + 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.