Unformatted text preview: ate inﬂection points? ture as a function of time is shown.
(a) Describe how the rate of population increase varies.
(b) When is this rate highest?
(c) On what intervals is the population function concave
upward or downward?
(d) Estimate the coordinates of the inﬂection point. 4. (a) State the First Derivative Test. (b) State the Second Derivative Test. Under what circumstances
is it inconclusive? What do you do if it fails? 700
yeast cells 300
100 5– 6 |||| The graph of the derivative f of a function f is shown.
(a) On what intervals is f increasing or decreasing?
(b) At what values of x does f have a local maximum or minimum? 5. 6. y 0 y y=fª(x) y=fª(x) s s 2 s 4 s 6 s x s 0 s 2 s s 4 s 6 s 4 6 8 10 12 14 16 18
Time (in hours) 11–20
0 2 |||| (a) Find the intervals on which f is increasing or decreasing.
(b) Find the local maximum and minimum values of f .
(c) Find the intervals of concavity and the inﬂection points. x s 11. f x x3 12 x 1 12. f x 5 3x 2 x3 S ECTION 4.3 HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH 13. f x x4 15. f x x 16. f x cos2 x 17. f x xe x 19. f x 2x2 x2 14. f x 3
0 31. x 2 sin x, y y=fª(x) 2 18. f x 2 x 2e x 20. f x ln x sx x ln x
0 s s s s s 305 (d) State the x-coordinate(s) of the point(s) of inﬂection.
(e) Assuming that f 0
0, sketch a graph of f. 3 3 2 sin x, x 2 ❙❙❙❙...
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This note was uploaded on 12/27/2013 for the course MATHEMATIC 135 taught by Professor Lam during the Fall '07 term at University of Toronto.
- Fall '07