Name - Berkeley City College

Berkeley City CollegeCalculus I - Math 3A - Chapter 3 Part 1 - The DerivativeHomework Due:___________ Sections 3.1 - 3.5Name___________________________________Calculate the instantaneous velocity for the given value of t of an object moving with rectilinear motion according to thegiven function relating s (in feet) and t (in seconds).1) s = 5t + 12; t = 41)A) -20 ft/s B) 5 ft/s C) 20 ft/s D) 32 ft/sObjective: (3.1) Calculate Instantaneous VelocityFind the derivative.5et2) s =2et + 12)A)5et(2et + 1)3B)5et(2et + 1)C)et(2et + 1)2D)5et(2et + 1)2Objective: (3.2) Find Derivative of Exponential3) y = 7 x2 + xe3)A) 2x 5/77+ exe B)27x5/7 + ex e C) 2x 5/7+ exe - 1 D)727x5/7 + ex e - 1Objective: (3.2) Find Derivative of Exponential14) y =x2.4 - π x4)A) -3.4x-2.4 + π 2 x -3/2 B) -2.4x-3.4 + π 2 x -3/2C) -2.4x-3.4 - π 2 x -3/2 D) -2.4x-3.4 + πx-3/2Objective: (3.2) Find Derivative of ExponentialInstructor: K. Pernell 1

5) w = z6 - e5)A) (6 - e)z5 - e B) z 7 - e7 - eC) z6 - e D) (5 - e)z6 - eObjective: (3.2) Find Derivative of ExponentialFind y ′.6) y = 1 x + 4 x - 1 x + 4A) 1 x3 + 4 B) - 1 x3 - 4 C) - 2 x3 - 4 D) 2 x3 + 4 6)Objective: (3.2) Find Derivative of Product7) y =1x2 + 6 x 2 - 1 x2 + 67)A) 4 x3 + 12x B) 4x5 + 12x C) - 1 x5 + 12x D) - 4 x5 - 12xObjective: (3.2) Find Derivative of ProductFind the derivative of the function.8) g(x) = x 2 + 5x2 + 6x8)A) g ′(x) = x 4 + 6x3 + 5x2 + 30xx2(x + 6)2B) g ′(x) = 6x 2 - 10x - 30x2(x + 6)2C) g ′(x) = 4x 3 + 18x2 + 10x + 30x2(x + 6)2D) g ′(x) = 2x 3 - 5x2 - 30xx2(x + 6)2Objective: (3.2) Find Derivative of Quotient2

9) f(t) = (4 - t)(4 + t3) -1A) f ′(t) = 2t 3 - 12t2 - 4(4 + t3) 2 B) f ′(t) = 2t 3 - 12t2 - 44 + t3C) f ′(t) = - 2t 3 + 12t2 - 4(4 + t3) 2 D) f ′(t) = - 4t 3 + 12t2 - 4Objective: (3.2) Find Derivative of Quotient(4 + t3) 2 9)10) y = x 2 - 3x + 2x7 - 210)A) y ′ = -5x 8 + 18x7 - 14x6 - 3x + 6(x7 - 2)2B) y ′ = -5x 8 + 18x7 - 14x6 - 4x + 6(x7 - 2)2C) y ′ = -5x 8 + 19x7 - 14x6 - 4x + 6(x7 - 2)2D) y ′ = -5x 8 + 18x7 - 13x6 - 4x + 6(x7 - 2)2Objective: (3.2) Find Derivative of QuotientFind the second derivative.11) y = 2x2 + 8x - 911)A) 4 B) 2 C) 0 D) 4x + 8Objective: (3.2) Find Second Derivative of Polynomial12) y = 6x2 + 7x + 5x-312)A) 12 - 60x-5 B) 12 + 60x-5 C) 12 + 60x-1 D) 12x + 7 - 15x-4Objective: (3.2) Find Second Derivative of Polynomial113) y =11x2 + 1 9x13)A)611x4 - 29x3B)611x4 + 29x3C) -211x4 + 19x3D) -211x3 - 19x2Objective: (3.2) Find Second Derivative of Polynomial3

14) r = 3s3 - 5 s14)A) 36s5 - 10s3B) 36s5 + 10s3C) - 9s4 + 5s2D) 3s5 - 5s3Objective: (3.2) Find Second Derivative of Polynomial15) s = 13t 33+ 1315)A) 13t2 B) 26t + 13 C) 26t D) 13tObjective: (3.2) Find Second Derivative of PolynomialFind Dxy.16) y = 1 2 x 10 - 1 5 x 516)A) 5x10 - x5 B) 5x11 - x6 C) 1 2 x 9 - 1 5 x 4 D) 5x9 - x4Objective: (3.3) Find Derivative Using Power/Sum/Difference Rules17) y = x7 + e717)A) 7x8 B) 7x7+ 7e7 C) 7x6 D) 7x6+ 7e6Objective: (3.3) Find Derivative Using Power/Sum/Difference Rules18) y = - 7x718)A) - 7x6 B) - 49x8 C) - 49x6 D) - 49x7Objective: (3.3) Find Derivative Using Power/Sum/Difference Rules19) y = 5x2 + 6x + 819)A) 10x2 + 6x + 8 B) 5x2 + 6 C) 10x + 6 D) 5x + 6Objective: (3.3) Find Derivative Using Power/Sum/Difference Rules4

20) y = x7A) 7x6 B) 6x6 C) 7x7 D) 6x 7 20)Objective: (3.3) Find Derivative Using Power/Sum/Difference Rules21) y = (6x - 5)(3x + 1)21)A) 18x - 9 B) 36x - 4.5 C) 36x - 21 D) 36x - 9Objective: (3.3) Find Derivative of Product22) y = (x2 - 4x + 2)(5x3 - x2 + 4)22)A) 25x4 - 80x3 + 42x2 + 4x - 16 B) 5x4 - 80x3 + 42x2 + 4x - 16C) 25x4 - 84x3 + 42x2 + 4x - 16 D) 5x4 - 84x3 + 42x2 + 4x - 16Objective: (3.3) Find Derivative of Productπ23) y =2x2 - 64πx4πxA) -(2x2 - 6) 2 B) -2x2 - 6C) 2πx 2 - 4πx - 6π(2x2 - 6) 2 D)Objective: (3.3) Find Derivative of Quotient23)6π - 4πx(2x2 - 6) 224) y =x3x - 524)A) -5x(3x - 5)2B) -53x - 5C) -5(3x - 5)2D)6x - 5(3x - 5)2Objective: (3.3) Find Derivative of Quotient5

25) y = x - 8x + 825)A)2x + 8B)16(x + 8)2C)8(x + 8)2D)16(x - 8)2Objective: (3.3) Find Derivative of Quotientπ26) y =5x2 - 4A)4π - 10πx(5x2 - 4) 2 B) -C) 5πx 2 - 10πx - 4π(5x2 - 4) 2 D) -Objective: (3.3) Find Derivative of Quotient26)10πx5x2 - 410πx(5x2 - 4) 227) y = 2x 2 + x - 1x3 - 4x227)A) -2x 4 - 2x3 + 7x2 - 8x(x3 - 4x2 ) 2 B) -2x 4 - 3x3 + 11x2 - 8x(x3 - 4x2 ) 2C) 10x 4 - 32x3 + 7x2 - 8x(x3 - 4x2 ) 2 D) 10x 4 - 2x3 + 7x2 - 8xx3 - 4x2Objective: (3.3) Find Derivative of Quotient28) y =x23 - 5x28)A) -15x 2 + 6x(3 - 5x)2B) 5x 3 - 10x2 + 6x(3 - 5x)2C)3x(3 - 5x)2D) -5x 2 + 6x(3 - 5x)2Objective: (3.3) Find Derivative of Quotient6

Find the equation of the tangent line to the equation at the point where x has the given value.29) y = 4x 2 - 63x - 2 ; x = 029)A) y = - 9 2 x - 3 B) y = 9 2 x + 3 C) y = - 9 2 x + 3 D) y = 9 2 x - 3Objective: (3.3) Find Equation of Tangent Line at a PointSolve the problem.30) At what points on the graph of y = 2x3 - 3x2 - 20x is the slope of the tangent line -8?30)A) (-1, 15), (1, -21) B) (0, 0), (2, -36) C) (1, -21), (15, 12) D) (-1, 15), (2, -36)Objective: (3.3) Find Points at Which Tangent Line Has Given Slope31) Find all points of the graph of y = 8x2 + 8x whose tangent lines are parallel to the line y - 24x = 0.31)A) (3, 96) B) (1, 16) C) (0, 0) D) (2, 48)Objective: (3.3) Find Points at Which Tangent Line Has Given Slope32) A cubic salt crystal expands by accumulation on all sides. As it expands outward find the rate ofchange of its volume with respect to the length of an edge when the edge is 0.210 mm.32)A) 0.132 mm3/mm B) 0.03 mm3/mm C) 13.20 mm3/mm D) 1.32 mm3/mmObjective: (3.3) Solve Apps: Derivative Rules33) The energy loss E (in joules/kilogram) due to friction when water flows through a pipe is given byE = 0.020(L/D)v2. In the formula, L is the pipe length (in m), D is the pipe diameter (in m), and v isthe water velocity (in m/s). Find a formula for the instantaneous rate of change of energy withrespect to velocity.33)A) dE/dv = 0.040(L/D)v2 B) dE/dv = (L/D)vC) dE/dv = 0.020(L/D)v D) dE/dv = 0.040(L/D)vObjective: (3.3) Solve Apps: Derivative Rules34) For a motorcycle traveling at speed v (in mph) when the brakes are applied, the distance d (in feet)required to stop the motorcycle may be approximated by the formula d = 0.050 v2 + v. Find theinstantaneous rate of change of distance with respect to velocity when the speed is 48 mph.34)A) 4.8 f/mph B) 11.6 f/mph C) 49 f/mph D) 5.8 f/mphObjective: (3.3) Solve Apps: Derivative Rules7

Find Dxy.35) y = x5 cos x - 10x sin x - 10 cos x35)A) -x5 sin x + 5x4 cos x - 10x cos x B) -x5 sin x + 5x4 cos x - 10x cos x - 20 sin xC) x5 sin x - 5x4 cos x + 10x cos x D) -5x4 sin x - 10 cos x + 10 sin xObjective: (3.4) Find Derivative of Trigonometric Function36) y = 9 x + 6 sec x36)A) 9 x2 - 6 sec x tan x B) - 9 x2+ 6 sec x tan xC) - 9 x2 - 6 csc x D) - 9 x2 + 6 tan 2xObjective: (3.4) Find Derivative of Trigonometric FunctionSolve the problem.37) Find the tangent to y = cos x at x = π 2 .37)A) y = - x - π 2B) y = x + π 2C) y = 1 D) y = - x + π 2Objective: (3.4) Solve Apps: Tangent LinesEvaluate the indicated derivative.38) fʹ(1/2) if f(x) = cos(πx) sin(πx)38)A) -π B) -1 C) π D) 0Objective: (3.5) Evaluate Derivative at a Point Using Chain Rule39) fʹ(2) if f(x) = (6 - x3) -139)A) - 6 B) - 3 C) 3 D) - 1 4Objective: (3.5) Evaluate Derivative at a Point Using Chain Rule8

Suppose that the functions f and g and their derivatives with respect to x have the following values at the given valuesof x. Find the derivative with respect to x of the given combination at the given value of x.40)40)x f(x) g(x) fʹ(x) gʹ(x)3 1 9 6 74 -3 3 2 -41/f2(x), x = 4A) - 1 4B)427C) - 4 27D) 2 27Objective: (3.5) Find Derivative Given Numerical Values41)x f(x) g(x) fʹ(x) gʹ(x)3 1 16 6 34 3 3 2 -6f(g(x)), x = 4A) 6 B) 18 C) -12 D) -36Objective: (3.5) Find Derivative Given Numerical Values41)Find Dxy.42) y = 1 5 (7x + 11) 342)A) 3 5 (7x + 11) 2 B) 215 (7x + 11) 2 C) 7 5 (7x + 11) 2 D) 215 x(7x + 11) 2Objective: (3.5) Find Derivative Using Chain Rule I43) y = (3x2 - 7) 343)A) 18x(3x2 - 7) 2 B) (18x - 7)(3x2 - 7) 2Objective: (3.5) Find Derivative Using Chain Rule I9

44) y = cos3(πx - 12)44)A) - 3π cos2(πx - 12) sin(πx - 12) B) - 3π sin2(πx - 12)C) - 3 cos2(πx - 12) sin(πx - 12) D) 3 cos2(πx - 12)Objective: (3.5) Find Derivative Using Chain Rule I45) y = sin 7πx2- cos 7πx245)A) 7π 2cos7πx2+ 7π 2sin7πx2B) 7π 2cos7πx2- 7π 2sin7πx2C) - 7π 2cos7πx2- 7π 2sin7πx2D) cos 7πx2+ sin 7πx2Objective: (3.5) Find Derivative Using Chain Rule I46) y = 3 7z + 8-9z + 746)A) - 7 277z + 8-9z + 7-2/3B) 1 37z + 8-9z + 7-2/3 121(-9z + 7)2C) 1 3121(-9z + 7)2-2/3D) 1 37z + 8-9z + 7-2/3Objective: (3.5) Find Derivative Using Chain Rule II47) y = 4x(3x + 5)347)A) 4(3x + 5)2 B) 4(3x + 5)3(6x + 5)C) 4(3x + 5)2(12x + 5) D) 4(12x + 5)2Objective: (3.5) Find Derivative Using Chain Rule IIFind an equation for the line tangent to the given curve at the indicated point.48) y = x3 - 36x + 4 at (6, 4)48)A) y = 72x + 4 B) y = 4 C) y = 72x - 428 D) y = 76x - 428Objective: (3.5) Find Equation of Tangent Line10

Find Dxy.49) e16xy + xy = 5[Hint: Use implicit differentiation]49)A) - 16e 16xy(x + y) + yxB) - 16ye 16xy + x + y16xe16xyC) - y xD) - 16ye 16xyxObjective: (3.9) Find Derivative of Exponential Function50) y =1ex950)A) - 9 x 8ex9B) 9 x 8ex9C) e-9x8D)1e9x8Objective: (3.9) Find Derivative of Exponential Function51) y = x6ex51)A) 6x5ex B) x5ex(1 + x) C) x5ex(6 + x) D) x5(6 + xex )Objective: (3.9) Find Derivative of Exponential Function52) y = e x + 852)A) 1 2x + 8 e x + 8 B) e x + 82 x + 8C) e(1/2 x + 8) D) e x + 8Objective: (3.9) Find Derivative of Exponential Function53) y = e(3 - 4x)53)A) e-4 B) 3e(3 - 4x) C) -4 ln (3 - 4x) D) -4e(3 - 4x)Objective: (3.9) Find Derivative of Exponential Function11

Answer KeyTestname: 12SPR_CH3_3.1TO3.5_PROBS1) B2) D3) D4) B5) A6) D7) B8) B9) A10) B11) A12) B13) B14) A15) C16) D17) C18) C19) C20) A21) D22) C23) A24) C25) B26) D27) A28) D29) B30) D31) B32) A33) D34) D35) A36) B37) D38) A39) C40) B41) D42) B43) A44) A45) A46) B47) C48) C49) C50) A12

Answer KeyTestname: 12SPR_CH3_3.1TO3.5_PROBS51) C52) B53) D13