find the constant c that makes g continuous (g in two parts)

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nona.m.nona
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Joined: Sun Dec 14, 2008 11:07 pm
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find the constant c that makes g continuous (g in two parts)

This is from my calculus book, but I think I only need algebra:

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?

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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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?
I'm not familiar with any extra, calc-specific stuff that you "should" do in addition to what you've done. And your value for "c" makes the two ends meet "in the middle", so your answer looks good to me!

Eliz.