If the function f(x) is differentiable and

f(x)=

{ax^3 + 6x, if x≤1

{$\displaystyle bx^2 + 4, if x>1$

then a =

What do I do?? No idea what's going on..

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- Jan 4th 2009, 08:57 AMelpermicHave no idea what to do..
If the function f(x) is differentiable and

f(x)=

{ax^3 + 6x, if x≤1

{$\displaystyle bx^2 + 4, if x>1$

then a =

What do I do?? No idea what's going on.. - Jan 4th 2009, 09:02 AMChris L T521
You need to do two things.

First, in order for it to be differentiable, it must be continuous at that point.

So you want to see where $\displaystyle \lim_{x\to1^-}f\left(x\right)=\lim_{x\to1^+}f\left(x\right)$.

Then. For it to be differentiable at that point, the slopes of the two piecewise functions must be the same at that point. This means that $\displaystyle 3a+6=2b$

You will then be able to come up with a system of equations. Now you can solve it for a.

Does this make sense? Can you take it from here? - Jan 4th 2009, 10:26 AMelpermic
I got my answer as b=4, a=2

I don't think it is right however.. - Jan 4th 2009, 10:47 AMChris L T521
- Jan 4th 2009, 10:48 AMskeeter
- Jan 4th 2009, 11:01 AMelpermic
a-b=-2

a-2b=-6 - Jan 4th 2009, 11:01 AMelpermic
- Jan 4th 2009, 11:33 AMskeeter
I get a = -2 also ... recheck the original function, make sure you copied it down correctly.

- Jan 4th 2009, 12:31 PMelpermic
Double checked, it is the same exact function as it says on my paper..

Don't know what's up with this one..