m2413c2 Multiple Choice Identify the choice that best completes the statement or answers the question 1 Find the derivative of the following function using the limiting process 2 Find the derivative of the following function using the limiting process 3 Find the derivative of the function by the limit process 4 Use the alternative form of the derivative to find the derivative of the function at 5 Find the derivative of the function 6 Find the slope of the graph of the function at the given valu when
7 Find the slope of the graph of the function at the given valu when 8 Find the slope of the graph of the function at 9 Find the slope of the graph of the function at 10 Determine all values of, (if any), at which the graph of the function has a horizontal tangent The graph has no horizontal tangents 11 Suppose the position function for a free-falling object on a certain planet is given by A silver coin is dropped from the top of a building that is 1370 feet tall Determine the velocity function for the coin 12 Use the Product Rule to differentiate 13 Find an equation of the tangent line to the graph of f at the given point 14 Find the second derivative of the function
18 Find the derivative of the function 15 Given the derivative below find the requested higher-order derivativ 16 Find the derivative of the function 19 Find the derivative of the function 20 Evaluate the derivative of the function 17 Find the derivative of the function at the point 21 Find by implicit differentiation
22 Find the slope of the tangent line at the given point decimal places 067 200 100 167 300 23 Find in terms of x and y Round your answer to two 25 Find the rate of change of the distance between the origin and a moving point on the graph of if centimeters per secon 24 Differentiate with respect to t (x and y are functions of t) 26 The radius r of a sphere is increasing at a rate of inches per minut Find the rate of change of the volume when r = inches
27 A spherical balloon is inflated with gas at the rate of cubic centimeters per minut How fast is the radius of the balloon increasing at the instant the radius is centimeters? 28 All edges of a cube are expanding at a rate of centimeters per secon How fast is the volume changing when each edge is centimeters? 29 An airplane is flying in still air with an airspeed of miles per hour If it is climbing at an angle of, find the rate at which it is gaining altitud Round your answer to four decimal places 30 Find by implicit differentiation
m2413c2 Answer Section MULTIPLE CHOICE 1 ANS: C PTS: 1 DIF: Medium REF: 2121 OBJ: Calculate the derivative of a function by the limit process NOT: Section 21 2 ANS: E PTS: 1 DIF: Medium REF: 2122 OBJ: Calculate the derivative of a function by the limit process NOT: Section 21 3 ANS: D PTS: 1 DIF: Difficult REF: 2124 OBJ: Calculate the derivative of a function by the limit process NOT: Section 21 4 ANS: E PTS: 1 DIF: Easy REF: 2173 OBJ: Calculate the derivative of a function at a specified point using the alternative form NOT: Section 21 5 ANS: B PTS: 1 DIF: Medium REF: 2221 OBJ: Differentiate trigonometric functions NOT: Section 22 6 ANS: E PTS: 1 DIF: Easy REF: 2231 NOT: Section 22 7 ANS: D PTS: 1 DIF: Medium REF: 2232 NOT: Section 22 8 ANS: A PTS: 1 DIF: Medium REF: 2234 NOT: Section 22 9 ANS: E PTS: 1 DIF: Medium REF: 2235 NOT: Section 22 10 ANS: C PTS: 1 DIF: Medium REF: 2260 OBJ: Calculate the values for which the slope of a function is zero NOT: Section 22 11 ANS: B PTS: 1 DIF: Medium REF: 2297a OBJ: Write the velocity function for a specified position function MSC: Application NOT: Section 22 12 ANS: D PTS: 1 DIF: Medium REF: 235 OBJ: Differentiate a function using the product rule NOT: Section 23 13 ANS: C PTS: 1 DIF: Medium REF: 2364a OBJ: Write an equation of a line tangent to the graph of a function at a specified point NOT: Section 23 14 ANS: A PTS: 1 DIF: Medium REF: 2398 OBJ: Calculate the second derivative of a function NOT: Section 23 15 ANS: C PTS: 1 DIF: Medium REF: 23103
OBJ: Calculate a higher derivative of a function NOT: Section 23 16 ANS: B PTS: 1 DIF: Medium REF: 248 OBJ: Differentiate a function using the chain rule NOT: Section 24 17 ANS: B PTS: 1 DIF: Medium REF: 2423 OBJ: Differentiate a function using the chain rule and product rule NOT: Section 24 18 ANS: E PTS: 1 DIF: Medium REF: 2426 OBJ: Differentiate a function using the chain rule and product rule NOT: Section 24 19 ANS: C PTS: 1 DIF: Easy REF: 2445 OBJ: Differentiate a function using the chain rule NOT: Section 24 20 ANS: E PTS: 1 DIF: Medium REF: 2472 OBJ: Evaluate the derivative of a function at a point NOT: Section 24 21 ANS: B PTS: 1 DIF: Medium REF: 2511 OBJ: Differentiate an equation using implicit differentiation NOT: Section 25 22 ANS: B PTS: 1 DIF: Difficult REF: 2530 OBJ: Evaluate the derivative of an implicit function at a given point NOT: Section 25 23 ANS: E PTS: 1 DIF: Easy REF: 2545 OBJ: Calculate the second derivative implicitly NOT: Section 25 24 ANS: B PTS: 1 DIF: Medium REF: 2568b OBJ: Differentiate an equation in x and y using implicit differentiation with respect to t NOT: Section 25 25 ANS: A PTS: 1 DIF: Medium REF: 2611 OBJ: Solve a related rate problem involving the distance between points NOT: Section 26 26 ANS: C PTS: 1 DIF: Easy REF: 2616a OBJ: Solve a related rate problem involving the volume of a sphere and its MSC: Application NOT: Section 26 27 ANS: C PTS: 1 DIF: Easy REF: 2617 OBJ: Solve a related rate problem involving the volume of a sphere and its radius MSC: Application NOT: Section 26 28 ANS: D PTS: 1 DIF: Easy REF: 2618 OBJ: Solve a related rate problem involving the volume of a cube and the length of a side MSC: Application NOT: Section 26 29 ANS: E PTS: 1 DIF: Medium REF: 2647 OBJ: Solve a related rate problem involving the altitude of an airplane MSC: Application NOT: Section 26 30 ANS: B PTS: 1 DIF: Easy REF: 251 OBJ: Differentiate an equation using implicit differentiation NOT: Section 25