How can I find the max/min of this function?

[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?

 

[Deleted member 4993]

---

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?

Good work...

However, I think you are making some mistake during inputing in your calculator. I am getting those to CPs to be (8.022, -2.4065) and (0.312, -0.0935).

There are additional CPs. What is the domain of f'(x)?