Using Excel Solver to find min cost?

[CanaBra]

Homework Statement

The cost production function as output, x, in 000's(where x>1.000) is given by the function
f(x)= 8x^3 + (352/x^2)-6x +6350

Homework Equations

USE THE EXCEL SOLVER function o determine the value of x which minimizes the cots. What is the cost at this point? What values of x will cause the cost to double?

The Attempt at a Solution

I have found the derivative of this function to be :
F'(x)= -704/x^3 + 24x^2-6

How do you solve this sort of function to find the minimum value of x?
If it was a squared only function, I could use the quadratic formula to find the inflection points, but this one after the first derivative is raised to the power of 3, what is the next step?

 

[Nino MMP]

I understand that this can be solved using the EXCEL SOLVER function, but I would really like to understand how to solve it by hand. Please would someone explain the steps to me?Thanks!