The value f x is the gradient at any point but often we want to find the Turning or StationaryPoint Maximum and Minimum points or Point of Inflection These happen where the gradient is zero f x 0. That is true and that is one rationale for thinking that hey we must have a maximum point assuming that our function is continuous at x equals negative four. A polynomial of degree n will have a maximum of n 1 turning points.
The function f x is maximum when f x 0 The function f x is minimum when f x 0 To find the maximum and minimum value we need to apply those x values in the given function.
Again using this graph you can see that the maximum point of the graph is at y 5. In calculus the derivative equals zero or does not exist at a functions maximum point. If. If the calculation is equal to 0 it is a point of inflection.