Theorem (Fermat Theorem).Given is a point defined on and differentiable at a point if has an extreme value (max. or min) , then . Note has maximum or minimum at . Definition 5. (a) A turning point is a maximum or minimum point. (b) If , then is called a critical or stationary value and its corresponding point on the graph is called stationary point. Notes 1. turning point stationary point 2. turning point + differentiable stationary point 3. stationary point turning point
|