# Homework Help: How can I find the max/min of this function?

1. Jun 3, 2013

### randy17

1. The problem statement, all variables and given/known data
Find the critical point of f(x)=(-5x^2+3x)/(2x^2-5), and show whether this point is a max/min.

2. Relevant equations

f(x)=(-5x^2+3x)/(2x^2-5)

3. The attempt at a solution
When I tried solving for the derivative of; f(x)=(-5x^2+3x)/(2x^2-5), I got (-6x^2+50x-15)/2x^2-5)^2.

then I set it equal to 0 and I got 0=-6x^2+50x-15

Now from here do I use the quadratic formula to solve for x? I tried that and I am getting x=(25+sqrt535)/6 and x=(25-sqrt535)/6. Have I done it right so far? When I try to plug in the x-values into the original eq to get y my calc says error... What do I do now?

2. Jun 3, 2013

### clamtrox

Try again. Everything looks OK.

3. Jun 3, 2013

### SteamKing

Staff Emeritus
Make sure you are using the right quadratic formula. Remember, it starts out with '-b', and your answers don't have the correct value for '-b'.

4. Jun 3, 2013

### MarneMath

The op's quadratic answer is correct.* If you're plugging in the exact formula into the calculator, I would simply instead just take an approximation of your answers (ie .311 and 8.02) and plug that in and then proceed with determining if the values are a max or a min.

*(The -b is negated by the 2a, where a is negative.)

Last edited: Jun 3, 2013
5. Jun 3, 2013

### Ray Vickson

Your answers are correct; it sounds like you need to buy a new calculator.

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