 Mathematics
W8 Calculus 20 Problems()

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1. f(x) = 0.2x2 - 2.4x + 5.9 A) Relative minimum at ( 6, 0) B) Relative minimum at ( 6, -1.3) C) Relative minimum at ( -6, 27.5) D) Relative maximum at ( 6, -1.3) 2. f(x) = (-5x + 7)4 A) f '(x) = 4(-5x + 7)3 B) f '(x) = -5(-5x + 7)3 C) f '(x) = -20(-5x + 7)3 3. D) f '(x) = -20(-5x + 7)4 f(x) = -6x2 - 2x - 7 A) Relative maximum at B) Relative maximum at C) Relative maximum at 4. D) Relative maximum at Differentiate. f(x) = (5x + 4)2 A) f'(x) = 2(5x + 4) B) f'(x) = 10(5x + 4) C) f'(x) = 10(5x + 4)2 D) f'(x) = 5(5x + 4) 5. f(x) = 5x + 9 at x = 2 A) f'(x) = 0; f'(2)=0 B) f'(x) = 9; f'(2) = 9 C) f'(x) = 5x; f'(2) = 10 6. D) f' (x) = 5; f' (2) = 5 Find the relative extrema of the function, if they exist. f(x) = x2 - 4x + 7 A) Relative maximum at ( 2, 3) B) Relative minimum at ( 2, 3) C) Relative maximum at ( 3, 2) D) Relative minimum at ( 3, 2) 7. f(x) = 6x + 2; [-1, 2] A) Absolute maximum: 12, absolute minimum: -6 B) There are no absolute extrema. C) Absolute maximum: 14, absolute minimum: -4 8. D) Absolute maximum: -1, absolute minimum: 2 A) B) C) D) 9. A) B) C) 10. D) f(x) = -3 - 7x; [-3, 1] A) There are no absolute extrema B) Absolute maximum: 18, absolute minimum: -10 C) Absolute maximum: 24, absolute minimum: -4 D) Absolute maximum: -10, absolute minimum: -24 11. A grocery store estimates that the weekly profit (in dollars) from the production and sale of x cases of is given by P(x) = -5600 + 9.5x - 0.0017x2 and currently 1300 cases are produced and sold per week. Use the marginal profit to estimate the increase in profit if the store prodcues and sells one additional case of soup per week. A) \$3877.00 B) \$7.29 C) \$5.52 12. D) \$5.08 Find the absolute maximum and absolute minimum values of the function, if they exist, ov indicated interval. When no interval is specified, use the real line (-∞, ∞). f(x) = -21; [ -7, 7] A) Absolute maximum: -21, absolute minimum: -21 B) There are no absolute extrema. C) Absolute maximum: 21, absolute minimum: -21 13. D) Absolute maximum: 21, absolute minimum: 0 s(x) = -x2 - 20x - 19 A) Relative maximum at ( -10, 81) B) Relative maximum at ( -20, -19) C) Relative minimum at ( 20, -19) D) Relative maximum at ( 10, 81) 14. A company estimates that the daily revenue (in dollars) from the sale of x cookies is given by R(x) = 885 + 0.02x + 0.0003x2 Currently, the company sells 900 cookies per day. Use marginal revenue to estimate the increase in revenue if the company increases sales by one cookie per day. A) \$92.00 B) \$56.00 C) \$0.92 D) \$0.56 15. A) B) C) D) 16. f(x) = 3 - 6x)140 A) f ' (x) = -840(3 - 6x)140 B) f ' (x) = 840(3 - 6x)139 C) f ' (x) = 4x; f ' (1) = 2 D) f ' (x) = -840(3 - 6x)139 17. A) B) C) D) 18. f(x) = x3 - 3x2 + 1 A) Relative minimum at (0, 1); relative maximum at (2, -3) B) Relative maximum at (2, -3) C) Relative maximum at (-2, -19); relative maximum at (0, 1) 19. D) Relative maximum at (0, 1); relative minimum at (2, -3) f(x) = 2x2 - 16x + 27 A) Relative minimum at ( -5, 4) B) Relative minimum at ( 5, -4) C) Relative minimum at ( 4, -5) D) Relative maximum at ( -4, 5) 20. Find the derivative of the function and evaluate the derivative at the given x-value. f(x) = 2x2 at x = 1 A) f' (x) = 4x; f' (1) = 4 B) f ' (x) = 2x; f ' (1) = 2 C) f' (x) = 4x; f' (1) = 2 D) f' (x) = 4x2; f' (1) = 4 ...
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