14b. Page 156 The Derivative 1-32 Odd

In Problems 1-5, find the indicated derivative.

1. y = 7x² + 2x -5, y'''

3. f(v) = (v² + 1)⁴ , f'''

5.

In Problems 7-11, find the indicated derivative and express the result in terms of x and y.

7. 2xy-y² = 5, d²y/dx².

9. x^2/3 + y^2/3 = 1, d²y/dx²

11.(x +y )² = 2xy + 5, d²y/dx²

In Problems 13 and 15, find f(x),f'(x),and f"(x) for the indicated value of x.

13. f(x) = 4x² -2x +1, x = 1

15.

In Problems 17 and 19, find dy/dx and d²y/dx² at the indicated point.

17. x² + y² = 25, (3,-4)

19.Ãx + Ãy = 1, (1/4, 1/4)

In Problems 21-27, position functions are given x in meters, t>0 in seconds, and the positive direction to the right. Analyze the motion as in Example 3, Page 155, and give a schematic diagram.

21. x = t³ - 2t² - 4t - 8

23. x = (t-3)³

25. x = 2t³ - 15 t² + 24 t

27.

In Problems 29 and 31, sketch the graphs of f'and f" if the following are graphs of f.