How Do You Find the Critical Point of f(x) = e^x - 5x^2 - ln(x)?

[jackchen]

Homework Statement

I'm stuck halfway in my differentiation.

The question is:
Suppose f(x) is the following function when x > 0, find the x-coordinate of the critical point of f(x).

Homework Equations

Equation = f(x) = e^x - 5x^2 - ln(x)

The Attempt at a Solution

I solved for: f'(x) = e^x - 10x - 1/x

From here on, I'm stuck. Help please?
Thank you! =)

 

[gb7nash]

Do you know bisection method? Newton's method?

 

[jackchen]

I'm afraid I don't. I'm very weak in Calculus, sorry!

 

[jackchen]

Do you know how I can solve this?
or where I can find a good explanation?

Thank you! =)

 

[gb7nash]

Unfortunately, this can't be solved algebraically. What do you set f'(x) equal to to find critical points? Also, a critical point is defined as a point where f'(x) is not defined. Where is that?

You'll need to resort to an iterative method such as bisection or Newton's method for the first one:

http://en.wikipedia.org/wiki/Bisection_method
http://en.wikipedia.org/wiki/Newton's_method