# Thread: Derivative Function Solve for a,b,c Problem

1. ## 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?

Is it $\displaystyle f(x) = \frac{ax+b}{x^2-c}$? or $\displaystyle \frac{ax+b}{x^2}-c$?

3. It is your first choice. All over $\displaystyle (x^2-c)$.

4. 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.

5. 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?

6. 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?

7. it seems that b would have to equal 9 so the function be equal to 0. Would that be correct?

8. 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.