From one extreme to the other

Tutorial on finding global extrema on closed intervals

Practice problems with solutions: finding global extrema on closed intervals

The topic of the day was finding local extrema of a function. General procedure: 1) Find the derivative of the function. 2) Find the critical values (values of x where the derivative of the function is either 0 or UNDEFINED). 3) Substitute values between the critical values into the derivative. (We used a number chart to demonstrate our results.) The function is increasing on the intervals when the derivative is positive. The function is decreasing on the intervals on which the derivative is negative. 4) Local mins occur at the critical values where the derivative changes from – to +. Local maxes occur at the critical values where the derivative changes from + to -. (Be sure the critical value is in the domain of the original function.)

Homework: page 192, #1-7 odd

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