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carla_ann26 · Aug 27, 2009, 04:22 PM

I am having a hard time with this math problem :(

g(x)=-x^2+9x
solve for g(a+h).

galactus · Aug 27, 2009, 04:39 PM

Just sub a+h in for x.

$g(a+h)=-(a+h)^{2}+9(a+h)$

I don't see anything to solve though.

Or are you trying to find the derivative of $-x^{2}+9x$ by using the definition of a derivative, but have it poorly worded?

The definition of a derivative is $g'(x)=\lim_{h\to 0}\frac{g(x+h)-g(x)}{h}$

Is that what you're getting at? Just a thought.

carla_ann26 · Aug 27, 2009, 04:50 PM

That's how far I got, now it's the "FOIL" and distributing stuff that I'm stuck on.

carla_ann26 · Aug 27, 2009, 04:53 PM

No... no derivatives involved here... It's more of a college algebra review.

galactus · Aug 28, 2009, 12:25 PM

I am not trying to be rude, but one learns FOIL in beginning algebra. You are in a calculus

class, so you may be in trouble. You had better see your instructor. The algebra is what

gives most students trouble in calculus. One should have algebra down pat before taking

calculus.

Upon subbing the a+h in for x, we can factor out an a+h

$-(a+h)(a+h-9)$ and expand

or just expand $-(a+h)^{2}+9(a+h)$

$= -(a+h)(a+h)+9(a+h)$

FOIL stands for First, Over, Inside, Last.

First would be $a\cdot a=a^{2} \;\ \text{Over}=a\cdot h, \;\ \text{Inside}=a\cdot h, \;\ \text{Last}=h^{2}$

Remember, the negative in the front. So, we have:

$=-a^{2}-2ah-h^{2}+9a+9h$