# How do you find the x coordinates of the turning points of the function?

Jun 9, 2018

I AM ASSUMING THAT YOUR FUNCTION IS CONTINUOUS AND DIFFERENTIABLE AT THE $x$ COORDINATE OF THE TURNING POINT

You can find the derivative of the function of the graph, and equate it to 0 (make it equal 0) to find the value of $x$ for which the turning point occurs.

#### Explanation:

When you find the derivative of a function, what you're finding is almost like a "gradient function", which gives the gradient for any value of $x$ that you want to substitute in.

Since the value of the derivative is the same as the gradient at a given point on a function, then with some common sense it's easy to realise that the turning point of a function occurs where the gradient (and hence the derivative) = 0.

So just find the first derivative, set that baby equal to 0 and solve it :-)