# Derivative Function Solve for a,b,c Problem

• Oct 15th 2009, 09:09 AM
r2d2
Derivative Function Solve for a,b,c Problem
Here's a Mind Teaser for everyone that certainly is teasing me right now..

Let $\displaystyle f$ be the function that is given by $\displaystyle f(x)= ax+b/x2-c$ and that has the following properties:

1. The graph of $\displaystyle f$ is symmetric with respect to the y-axis (meaning f(x)=f(-x)?)

2. Lim x→3 f(x)= -∞

3. $\displaystyle f'(-2)= -4$

a.) Determine the values of a,b, and c.
b.) Write an equation for each vertical and each horizontal asymptote of the graph $\displaystyle f$.

ATTEMPT:
So I determine that $\displaystyle a$ must equal 0 because if the graph is symettric about the y-axis, that means (x) must equal (-x). I solved for a, and got a=-a, where a=0.

Then I get lost. Where would I go from there?
• Oct 15th 2009, 09:13 AM
Defunkt

Is it $\displaystyle f(x) = \frac{ax+b}{x^2-c}$? or $\displaystyle \frac{ax+b}{x^2}-c$?
• Oct 15th 2009, 09:19 AM
r2d2
It is your first choice. All over $\displaystyle (x^2-c)$.
• Oct 15th 2009, 09:27 AM
Defunkt
Quote:

Originally Posted by r2d2
It is your first choice. All over $\displaystyle (x^2-c)$.

OK then. a=0 is correct, so we have $\displaystyle f(x) = \frac{b}{x^2-c}$...

First, think what could cause $\displaystyle \lim_{x\to3}f(x) = -\infty$? One part of the function has to go "wild" -- could it be the numerator? or the denominator? and why?

Second, find the derivative and substitute the given value to find the last constant.
• Oct 15th 2009, 09:32 AM
r2d2
Ok. It actually says the limit as x approaches 3 from the left. Would that mean the denominator would go to 0, meaning that $\displaystyle c$ would be 9?
• Oct 15th 2009, 09:39 AM
Defunkt
Quote:

Originally Posted by r2d2
Ok. It actually says the limit as x approaches 3 from the left. Would that mean the denominator would go to 0, meaning that $\displaystyle c$ would be 9?

Yes, that is correct. Can you find b now?
• Oct 15th 2009, 09:42 AM
r2d2
it seems that b would have to equal 9 so the function be equal to 0. Would that be correct?
• Oct 15th 2009, 09:53 AM
Defunkt
Quote:

Originally Posted by r2d2
it seems that b would have to equal 9 so the function be equal to 0. Would that be correct?

It says nowhere that the function needs to equal 0. You need to find the derivative and solve $\displaystyle f'(-2)=-4$ with regards to b.