969 Chapter 13 Curve Sketching PROBLEMS 13.3 In Problems 1-6, a function and its second derivative are given. Determine the concavity of f and find x-values where points of inflection occur. 1. f(x) = x* – 3x – 6x² + 6x + 1; f"(x) = 6(2x+ 1)(x – 2) %3D - 2. f(x) – 2x²; f"(x) = (x – 1)(x+ 2)² - %3D %3D 4 20 2+x – x² (x – L)) (x),L:+x7 - zr (x – 1)4 2(2x+ 1 - 3. f(x) = - x² = (x)f ' (x– 1)2if"(x) (x - 1)4 6(3x² + 2) - = (x),f:?- = (x)S 's (x² – 2)3 x² - %3D - x(2x² – 3a?) (a² – x²)3/2 In Problems 7-34, determine concavity and the x-values where 6. f(x) = xva? – x²; f"(x) = - %3D - points of inflection occur. Do not sketch the graphs. 7. y = -2x2 + 4x 9. y= 4x + 12x² – 12x 11. y = ax + bx² + cx+d__12. y = x - 8x2 -6 8. y = -74x²+ 19x- 37 %3D 10. y = x'- 6x² + 9x + 1 %3D %3D | 13. y = 2x-48x2 + 7x+3 14. y = 9x2 --+ + 2x 4. a. 15. y = 2r/5 2.

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