# I need help with 1-20

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I need help with 1-20

I need help with 1-20

Intro to Derivatives Worksheet Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the definition f'(a) = lim h -> 0 f(a + h) – f(a) h to find the derivative of the given function at the given value of a. 1) f(x) = – 4 /x, a = 9 1) A) 81 4 B) 9 4 C) 4 9 D) 4 81 2) f(x) = 4 – 3 x 2 , a = 3 2) A) 18 B) 22 C) – 18 D) – 14 3) f(x) = x 3 + 3 , a = 5 3) A) 78 B) – 75 C) 76 D) 75 4) f(x) = 8 x 2 , a = 1 4) A) – 16 B) 16 C) 8 D) – 8 5) f(x) = 12 – 14 x, a = 1 5) A) 12 B) – 12 C) – 2 D) – 14 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 6) f(x) = 3 x 2 , a = 1 6) 7) f(x) = – 7 /x, a = 6 7) 8) f(x) = 7 – 4 x 2 , a = 3 8) 9) f(x) = x 3 + 3 , a = 2 9) 10) f(x) = 17 – 16 x, a = 1 10) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 11) Find d dx (x 2 + 9 ). 11) A) 2 x 2 B) 2x C) 2x + 9 D) x + 9 12) Find dy/dx if y = 5 – 8 x. 12) A) dy/dx = 5 – 8 x B) dy/dx = – 3 C) dy/dx = – 8 D) dy/dx = – 8 x 1 13) Find d dx ( 2 x 2 + 9 ). 13) A) 2 x B) 4 x C) 4 x + 9 D) 4 x 2 + 9 14) Find f'(x) if f(x) = 7 x – 24 . 14) A) f'(x) = 7 x B) f'(x) = 7 C) f'(x) = – 17 D) f'(x) = – 7 15) Find dy/dx if y = 17 – 19 x. 15) A) dy/dx = – 2 B) dy/dx = – 19 x C) dy/dx = – 19 D) dy/dx = 17 – 19 x SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 16) Find d dx ( 4 x 2 – 5 ). 16) 17) Find f'(x) if f(x) = 20 x – 16 . 17) 18) Find d dx (x 2 – 6 ). 18) 19) Find d dx ( 2 x 2 – 3 ). 19) 20) Find f'(x) if f(x) = 12 x – 7 . 20) 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of a function is given. Choose the answer that represents the graph of its derivative. 21) 21) A) B) C) D) 3 22) 22) A) B) C) D) 4 23) 23) A) B) C) D) 5 24) 24) A) B) C) D) 6 25) 25) A) B) C) D) Solve the problem. 26) Find an equation of the tangent line to the graph of y = x 2 – x, at the point ( – 3 , 12 ). 26) A) y = – 7 x – 6 B) y = – 7 x + 9 C) y = – 7 x + 6 D) y = – 7 x – 9 27) Find an equation of the tangent line to the graph of y = x – x 2 at the point ( 4 , – 12 ). 27) A) y = 9x – 16 B) y = 9x + 16 C) y = – 7x + 16 D) y = 7x + 16 28) If y = x 2 – 3 , find an equation of the tangent line to the graph of y at x = – 2 . 28) A) y = – 2 x – 7 B) y = – 4 x – 11 C) y = – 4 x – 7 D) y = – 4 x – 14 29) If y = x 2 + 3 , find an equation of the tangent line to the graph of y at x = 3 . 29) A) y = 6 x – 15 B) y = 3 x – 6 C) y = 6 x – 6 D) y = 6 x – 12 7 30) If y = x 3 – 36 x + 4 , find an equation of the tangent line to the graph of y at x = 6 . 30) A) y = 4 B) y = 72 x + 4 C) y = 72 x – 428 D) y = 76 x – 428 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 31) Find an equation of the tangent line to the graph of y = 10 x – x + 7 at the point ( 100 , 7 ). 31) 32) If y = x 2 – 3 , find an equation of the tangent line to the graph of y at x = 4 . 32) 33) If y = x 2 + 3 , find an equation of the tangent line to the graph of y at x = – 2 . 33) 34) Find an equation of the tangent line to the graph of y = x 2 – x, at the point ( 3 , 6 ). 34) 35) If y = x 3 – 25 x – 1 , find an equation of the tangent line to the graph of y at x = 5 . 35) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 36) Find the equation of the normal line to the curve y = 3 x + 4 x 2 at the point ( – 4 , 52 ). 36) A) x – 29 y + 1512 = 0 B) x + 35 y + 1512 = 0 C) x + 35 y + 2664 = 0 D) x – 29 y + 2664 = 0 37) Find the equation of the normal line to the graph of y = 3 x 2 at x = – 5 . 37) A) x – 30 y + 2255 = 0 B) x – 30 y – 2245 = 0 C) x – 30 y + 2245 = 0 D) x + 30 y – 2245 = 0 38) Find the equation of the normal line to the curve y = 3 – 4 x 3 at the point ( – 2 , 35 ) 38) A) x + 48 y – 1682 = 0 B) x + 48 y + 1682 = 0 C) x – 48 y + 1682 = 0 D) x – 48 y – 1682 = 0 39) Find the equation of the normal line to the graph of y = 3 x 2 at x = – 2 . 39) A) x + 12 y – 142 = 0 B) x – 12 y – 142 = 0 C) x – 12 y + 142 = 0 D) x – 12 y + 146 = 0 40) Find the equation of the normal line to the curve y = 3 – 4 x 3 at the point ( 4 , – 253 ) 40) A) x – 192 y – 48,580 = 0 B) x + 192 y + 48,580 = 0 C) x + 192 y – 48,580 = 0 D) x – 192 y + 48,580 = 0 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 41) Find the equation of the normal line to the curve y = 3 x – 4 x 2 at the point ( – 4 , – 76 ). 41) 42) Find the equation of the normal line to the graph of y = 3 x 2 at x = 4 . 42) 43) Find the equation of the normal line to the curve y = 5 – 2 x 3 at the point ( – 3 , 59 ) 43) 8 44) Find the equation of the normal line to the curve y = 4 x – 2 x 2 at the point ( 2 , 0 ). 44) 45) Find the equation of the normal line to the curve y = 3 – 3 x 3 at the point ( 5 , – 372 ) 45) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 46) Assume that a watermelon dropped from a tall building falls y = 16 t 2 feet in t seconds. Find the watermelon’s average speed during the first 3 seconds of fall and the speed at the instant t = 3 seconds. 46) A) 24 ft/sec; 48 ft/sec B) 48 ft/sec; 96 ft/sec C) 96 ft/sec; 49 ft/sec D) 49 ft/sec; 98 ft/sec 47) The equation for free fall at the surface of Planet X is s = 11.76 t 2 meters with t in seconds. Assume a rock is dropped from the top of a 600 – meter cliff. Find the speed of the rock at t = 2 seconds. 47) A) 22.52 m/sec B) 23.52 m/sec C) 48.04 m/sec D) 47.04 m/sec 48) A cubic salt crystal expands by accumulation on all sides. As it expands outward find the rate of change of its volume with respect to the length of an edge when the edge is 0.19 millimeter. 48) A) 0.02 mm 3 /mm B) 10.83 mm 3 /mm C) 0.1083 mm 3 /mm D) 1.08 mm 3 /mm 49) A balloon used in surgical procedures is cylindrical in shape. As it expands outward, assume that the length remains a constant 80.0 millimeters . Find the rate of change of surface area with respect to radius when the radius is 0.080 millimeter. (Express answer in terms of ” ). 49) A) 80.32 ” mm 2 /mm B) 80.16 ” mm 2 /mm C) 160.0 ” mm 2 /mm D) 160.32 ” mm 2 /mm 50) Sue planted a vegetable garden in 2000. The table shows the number of vegetables her garden produced each year until 2005. Let the point (0, 33 ) represent 2000, the point (1, 39 ) represent 2001, and so on. Find the slope of the secant line from 2000 to 2005 . Round to the nearest hundredth when necessary. Year Vegetables produced 2000 33 2001 39 2002 52 2003 46 2004 60 2005 68 50) A) 20.2 B) 3.5 C) 7 D) 0.14 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 51) 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 = 0.05 v 2 + v. Find the instantaneous rate of change of distance with respect to velocity when the speed is 41 mph. 51) 9 52) John began keeping track of the amount of money he spent annually at his local coffee shop. The table shows his yearly spending from 2005 to 2010. Find the average rate of change from 2005 to 2008 . Round to the nearest cent. Year Money Spent (dollars) 2005 499 2006 548 2007 594 2008 618 2009 516 2010 548 52) 53) The equation for free fall at the surface of Planet X is s = 2.71 t 2 meters with t in seconds. Assume a rock is dropped from the top of a 600 – meter cliff. Find the speed of the rock at t = 5 seconds. 53) 54) Assume that a watermelon dropped from a tall building falls y = 16 t 2 feet in t seconds. Find the watermelon’s average speed during the first 4 seconds of fall and the speed at the instant t = 4 seconds. 54) 55) A cubic salt crystal expands by accumulation on all sides. As it expands outward find the rate of change of its volume with respect to the length of an edge when the edge is 0.31 millimeter. 55) 10 Answer Key Testname: INTRO_DERIVATIVES WS 1) D 2) C 3) D 4) B 5) D 6) 6 7) 7 36 8) – 24 9) 12 10) – 16 11) B 12) C 13) B 14) B 15) C 16) 8 x 17) f'(x) = 20 18) 2x 19) 4 x 20) f'(x) = 12 21) C 22) B 23) C 24) D 25) C 26) D 27) C 28) C 29) C 30) C 31) y = – 1 2 x + 57 32) y = 8 x – 19 33) y = – 4 x – 1 34) y = 5 x – 9 35) y = 50 x – 251 36) A 37) A 38) C 39) D 40) A 41) x + 35 y + 2664 = 0 42) x + 24 y – 1156 = 0 43) x – 54 y + 3189 = 0 44) x – 4 y – 2 = 0 45) x – 225 y – 83,705 = 0 46) B 47) D 11 Answer Key Testname: INTRO_DERIVATIVES WS 48) C 49) D 50) C 51) 5.1 mph 52) $39.67 dollars per year 53) 27.1 m/sec 54) 64 ft/sec; 128 ft/sec 55) 0.2883 mm 3 /mm 12

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