Given that f(x)={8+x^3 when x1} Determine the values of the constants B and C so that f is differentiable.

Question

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.

anonymous · Answer

first plug in 1 to both
what do you get?

clara1223 · Answer

I get 9 and B+C

anonymous · Answer

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

anonymous · Answer

did i lose you there?

clara1223 · Answer

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 · Answer

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

anonymous · Answer

there is an $x$ in $Bx+C$ for sure

clara1223 · Answer

oh you mean before i plugged in 1, gotcha.

anonymous · Answer

oh yes before

clara1223 · Answer

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 · Answer

yes plug in 1 to both 
you should get 
$$B=3$$

anonymous · Answer

making $A=6$ and you are done