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

Question

Christopher Allers · Accepted Answer

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.

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 :-)

Evelyn Agard · Answer

undefined To find the x-coordinates of the turning points of a function, you need to first find the derivative of the function. Then, set the derivative equal to zero and solve for the x-values. These x-values are the potential turning points. To determine whether each potential turning point is a minimum, maximum, or neither, you can use the second derivative test or analyze the behavior of the function around each point. If the second derivative is positive at a potential turning point, it indicates a minimum; if it's negative, it indicates a maximum. If the second derivative is zero or undefined, further analysis is required.