W E SAY THAT A FUNCTION f(x) has a relative maximum value at x = a, if f(a) is greater than any value immediately preceding or follwing.. We call it a "relative" maximum because other values of the function may in fact be greater. This is a PowerPoint presentation that leads through the process of finding maximum and minimum points using differentiation. It gradually builds the difficulty until students will be able to find turning points on graphs with more than one turning point and use calculus to determine the nature of the turning points. $\begingroup$ THe question asks for proof of a maximum turning point at $(\frac{\pi}2, 1)$ and a minimum turning point of $(\frac{3\pi}2, -1)$ $\endgroup$ – dagda1 Apr 15 '16 at 19:16 $\begingroup$ @dagda1 The argument given here is based on the Second Derivative Test . It starts off with simple examples, explaining each step of the working. Points of Inflection. $\endgroup$ – N. F. Taussig Apr 15 '16 at 21:26

The value f '(x) is the gradient at any point but often we want to find the Turning or Stationary Point (Maximum and Minimum points) or Point of Inflection These happen where the gradient is zero, f '(x) = 0.
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Free functions turning points calculator - find functions turning points step-by-step This website uses cookies to ensure you get the best experience. 10. MAXIMUM AND MINIMUM VALUES The turning points of a graph. Critical Points include Turning points and Points where f ' (x) does not exist.