clara1223
  • 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.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
first plug in 1 to both what do you get?
clara1223
  • clara1223
I get 9 and B+C
anonymous
  • 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
  • anonymous
did i lose you there?
clara1223
  • 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
  • clara1223
how do you find a derivative if there is no x?
anonymous
  • anonymous
there is an \(x\) in \(Bx+C\) for sure
clara1223
  • clara1223
oh you mean before i plugged in 1, gotcha.
anonymous
  • anonymous
oh yes before
clara1223
  • 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
  • anonymous
yes plug in 1 to both you should get \[B=3\]
anonymous
  • anonymous
making \(A=6\) and you are done

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