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

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

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.

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 I don't understand your question. – Mariano Suárez-Alvarez♦ Feb 12 at 6:33 extrema of a differentiable function are at the roots of the derivative. – Memming Feb 12 at 15:43