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**Extra resources for 550 AP Calculus AB & BC Practice Questions (College Test Preparation)**

The curve y = ax3 + bx2 + cx + d passes in the course of the element (2, eight) and is basic to y = − x − four at (0, –4). If b = five, what's the price of a? (A) –2 (B) − (C) − (D) –1 (E) − 14. At what time does the particle swap path if the location functionality is given by means of x(t) = 2x4 − 4x3 + 2x2 − eight, the place t > zero? (A) (B) 1 (C) (D) 2 (E) 15. what's the particle’s speed at t = three if and x = 3x3 − 2x2 + four and y = 2x2 + 3x − 7? (A) 69 (B) 15 (C) (D) 4 (E) sixteen. Use differentials to approximate (5. 2)3. (A) 125 (B) 130 (C) 135 (D) 140 (E) 145 17. The radius of a cylinder is elevated from nine to nine. 03 inches. If the peak continues to be consistent at 12 inches. Estimate the switch in quantity. (A) 0. 005π in3 (B) 3. 24π in3 (C) 6. forty eightπ in3 (D) 9π in3 (E) 12π in3 18. Use differentials to approximate cos275°. (A) (B) (C) (D) (E) 19. locate the size of the curve y = from x = zero to x = 6. (A) (B) 20 (C) (D) (E) 21 20. If x2 + y2 = 25, then locate the slope of the tangent that passes during the point(2,4). (A) –1 (B) – (C) 0 (D) (E) 1 21. locate the equation of the tangent line to the curve x2 + xy + y2 = three at (1,1). (A) 3x – y = 2 (B) x – y = 2 (C) 3x + y = 2 (D) x + y = 2 (E) x – 3y = –2 22. what's the slope of the road common to the curve f(x) = x4 + 3x2 that passes during the aspect (2,1)? (A) 44 (B) (C) 0 (D) – (E) –44 23. What dimensions needs to a rectangle need to maximize the realm and feature a fringe of a hundred meters? (A) 40 m by way of 10 m (B) 45 m by way of five m (C) 35 m via 15 m (D) 30 m by way of 20 m (E) 25 m by means of 25 m 24. What confident numbers not just yield a minimal sum, but in addition produce a manufactured from a hundred? (A) 50 and a couple of (B) 25 and four (C) 10 and 10 (D) 20 and five (E) 100 and 1 25. What numbers either have a sum of 23 and a product that's maximized? (A) 12 and eleven (B) 11. five and eleven. five (C) 10 and thirteen (D) 9. five and thirteen. five (E) 8 and 15 26. If y = 4x3 – 9x2 + 6x, then what's the price of the relative minimal, if any? (A) –1 (B) 0 (C) (D) 1 (E) 2 bankruptcy sixteen functions of Derivatives Drill 2 solutions and factors resolution KEY 1. E 2. B three. A four. D five. A 6. E 7. C eight. A nine. E 10. A eleven. A 12. B thirteen. B 14. B 15. C sixteen. D 17. C 18. B 19. D 20. B 21. D 22. D 23. E 24. C 25. B 26. D factors 1. E First, you need to take the by-product of the given functionality, maintaining in brain undefined, b, and c all signify constants, now not variables. y = ax2 + bx + c y′ = 2ax + b Given the two coordinates and their respective slopes, you could get a hold of linear equations bearing on a and b, that are solved to figure out the person values. y′ (–1) = 2a(–1) + b = 6 and y′ (5) = 2a(5) + b = –2 So, the equations are –2a + b = 6 and 10a + b = –2. Stack the equations on best of each other to begin fixing for the constants. you could cast off b completely by means of subtracting the 2 equations. Plugging the worth of a into both equation yields b = .