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- clara1223

Given that f(x)={8+x^3 when x<=1 and Bx+C when x>1} Determine the values of the constants B and C so that f is differentiable.

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- clara1223

- katieb

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- anonymous

first plug in 1 to both
what do you get?

- clara1223

I get 9 and B+C

- anonymous

ok so you have one equation
\[B+C=9\]
now take the derivative of both and then plug in 1

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- anonymous

did i lose you there?

- clara1223

sorry I had to restart my computer, it was being weird. But using the shortcut I get that both derivatives are 0 because there are no xs

- clara1223

how do you find a derivative if there is no x?

- anonymous

there is an \(x\) in \(Bx+C\) for sure

- clara1223

oh you mean before i plugged in 1, gotcha.

- anonymous

oh yes before

- clara1223

what do i do after I get the derivative and plug in 1? I need to go do something before i finish this problem but im guessing you wont be online later so i was hoping you could explain really quickly so i will know how to do it later.

- anonymous

yes plug in 1 to both
you should get
\[B=3\]

- anonymous

making \(A=6\) and you are done

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