121616949-math.111

# 121616949-math.111 - 5.2 The first derivative test 97...

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5.2 The first derivative test 97 Exercises In problems 1–12, find all local maximum and minimum points ( x, y ) by the method of this section. 1. y = x 2 - x 2. y = 2 + 3 x - x 3 3. y = x 3 - 9 x 2 + 24 x 4. y = x 4 - 2 x 2 + 3 5. y = 3 x 4 - 4 x 3 6. y = ( x 2 - 1) /x 7. y = 3 x 2 - (1 /x 2 ) 8. y = cos(2 x ) - x 9. f ( x ) = x - 1 x < 2 x 2 x 2 10. f ( x ) = 8 < : x - 3 x < 3 x 3 3 x 5 1 /x x > 5 11. f ( x ) = x 2 - 98 x + 4 12. f ( x ) = - 2 x = 0 1 /x 2 x = 0 13. Recall that for any real number x there is a unique integer n such that n x < n + 1, and the greatest integer function is given by x = n , as shown in figure 3.1 . Where are the critical values of the greatest integer function? Which are local maxima and which are local minima? 14. Explain why the function f ( x ) = 1 /x has no local maxima or minima. 15. How many critical points can a quadratic polynomial function have? 16. Show that a cubic polynomial can have at most two critical points. Give examples to show that a cubic polynomial can have zero, one, or two critical points.
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