The Extreme Points Calculator helps identify local maxima and minima of a function by examining its critical points and the behavior of its derivative.
Finding extreme points
For a differentiable function f(x), first solve f'(x) = 0. Points where the derivative does not exist may also be critical points. These candidates are then tested to determine whether they are local maxima, local minima, or neither.
Worked example
Consider f(x) = xΒ² - 4x + 1. Its derivative is f'(x) = 2x - 4. Setting the derivative to zero gives x = 2. Substituting into the original function gives f(2) = -3, so the curve has a minimum at (2, -3).
How to check the result
If the derivative changes from negative to positive, the critical point is a local minimum. A change from positive to negative indicates a local maximum. The second derivative can also help when its value is nonzero at the critical point.