Why Local Minimum is calculated for a derivative function instead of actual function?

Question

In Machine learning regression problem, why the local minimum is computed for a derivative function instead of the actual function?

Example: http://en.wikipedia.org/wiki/Gradient_descent

The gradient descent algorithm is applied to find a local minimum of the function $$

$f(x)=x^4−3x^3+2,$ ----(A)

with derivative

$f'(x)=4x^3−9x^2.$ ----(B)

Here to find the local minimum using gradient descent algorithm for the function $(A)$ they have used the derivative function of $(A)$ which is function $(B)$.

Hope this one is clear.