# Exercise: Using Gradient Descent to Minimize a Cost Function

Learn how to use the gradient descent method to minimize the cost function.

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## Approach to minimize the cost function

In this exercise, our task is to find the best set of parameters in order to minimize the following hypothetical cost function: $y = f(x) = x^2 â€“ 2x$. To do this, we will employ gradient descent, which was described in the preceding lesson. Perform the following steps to complete the exercise:

1. Create a function that returns the value of the cost function and look at the value of the cost function over a range of parameters. You can use the following code to do this:

X_poly = np.linspace(-3,5,81)
print(X_poly[:5], '...', X_poly[-5:])
def cost_function(X):
return X * (X-2)
y_poly = cost_function(X_poly)
plt.plot(X_poly, y_poly)
plt.xlabel('Parameter value')
plt.ylabel('Cost function')
plt.title('Error surface')


You will obtain the following plot of the cost function:

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