MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. D) g (x) = - 2 x2 ; g (- 2) = C) 21 4

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1 Cal 1: Test review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Calculate the derivative of the function. Then find the value of the derivative as specified. 1) g() = - ; g (-) 1) g () = - ; g (- ) = - B) g () = - ; g (- ) = - 8 g () = ; g (-) = 1 D) g () = - ; g (- ) = - 1 Find the slope of the tangent line at the given value of the independent variable. ) f() = 3 + 9, = ) 3 B) 3 1 D) 1 Find an equation of the tangent line at the indicated point on the graph of the function. 3) = f() = - + 1, (, ) = (0, 1) = 1-1 B) = = D) = 1 3) Find the slope of the line tangent to the curve at. 6 ) = + ; = 3 ) 6 B) D) - 1 Find D. ) = B) D) ) 6) = (1-3)(3-36) B) D) ) 7) = ( - + )(3 - + ) B) D) ) 8) = (3 + 8) B) D) ) 1

2 The graph of a function is given. Choose the answer that represents the graph of its derivative. 9) 1 9) B) D) Given the graph of f, find an values of at which f is not defined. ) ) = -3, 0, 3 B) = -3, 3 = -, D) = -, 0,

3 Find. 11) = (3 + 6)(7-8) B) D) ) Find D. π 1) = 7-8 1π 1π - (7-8) B) π - 1π (7-8) D) 7π - 1π - 8π (7-8) 1) 13) = ) (3-9 ) B) (3-9 ) D) (3-9 ) 1) = (sec + tan )-3-3(sec + tan )- B) -3(sec tan + sec) - 1) -3 sec (sec + tan )3 D) -3(sec + tan )-(tan + sec tan ) Find the absolute etreme values of each function on the interval. 1) = 6-7 on [-3, ] Maimum = (0, ); minimum = (-3,-7) B) Maimum = (0, 6); minimum = (,-6) Maimum = (0, 7); minimum = (,-118) D) Maimum = (0, 1); minimum = (,-7) 1) Find D. 16) = cos7(π - 0) - 7π cos6(π - 0) sin(π - 0) B) 7 cos6(π - 0) - 7π sin6(π - 0) D) - 7 cos6(π - 0) sin(π - 0) 16) 17) = cos sin 6 cos 1 + sin sin cos B) - sin cos D) - 6 cos (1 + sin )6 cos 1 + sin 17) 3

4 18) = 3 z + 6-9z z + 6-9z (-9z + 3) -/3 -/3 B) 1 3 D) - 7 z + 6-9z + 3 z + 6-9z + 3 -/3 69 (-9z + 3) -/3 18) 19) = 3( + 3)3 3( + 3) B) 3( + 3)3(7 + 3) 3(16 + 3) D) 3( + 3)(16 + 3) 19) Evaluate the indicated derivative. 0) f'() if f() = B) 18 7 D) ) 1) f'() if f() = (3-3) -1 1 B) D) - 1 1) Find an equation for the line tangent to the given curve at the indicated point. ) = - at (, ) = B) = 3-6 = 3 - D) = 3 + ) 3) = at (3,-) = 18-8 B) = - = 18 - D) = 1-8 3) Find the indicated derivative of the function. ) d 3 d3 for = ( - ) B) D) ) ) d d for = sin 16 sin B) sin cos D) - sin ) Assuming that the equation defines a differential function of, find D b implicit differentiation. 6) - = 1 - B) - - D) - 6) 7) + + = - + B) D) )

5 8) 6 = cot 6 csc B) csc 6-6 csc D) - 6 csc cot 8) Find an equation for the line tangent to the given curve at the indicated point. 9) = 8 at (, 0) = 1 ( - ) B) = 0 = D) = - 3 ( - ) 9) 30) + 3 = + 11 at (0, 1) = B) = = D) = ) Find d d. 31) = (6 + ) 1/3 36 (6 + ) 1/3 B) (6 + ) / (6 + ) /3 D) 36 + (6 + ) /3 31) Use implicit differentiation to find ". 3) - + = 3 + B) ( + 1) + 1 ( + 1) 1 - ( + 1) D) - ( + 1) 3) 33) - + = 3 - ( + ) B) + 1 ( + ) + ( + ) D) ) Solve the problem. Round our answer, if appropriate. 3) One airplane is approaching an airport from the north at 01 km/hr. A second airplane approaches from the east at km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 8 km awa from the airport and the westbound plane is km from the airport. -3 km/hr B) -6 km/hr -60 km/hr D) -1 km/hr 3) 3) A ladder is slipping down a vertical wall. If the ladder is 0 ft long and the top of it is slipping at the constant rate of ft/s, how fast is the bottom of the ladder moving along the ground when the bottom is 16 ft from the wall? 0.8 ft/s B) 3.0 ft/s 0. ft/s D).0 ft/s 3) Find d. 36) = d B) + d + 9 d D) ( + ) d 36)

6 37) = d B) 1-16 d d D) + 8 d 37) Find all critical points and find the minimum and maimum value of the function on the given domain. 38) Domain: [-, 3] 38) Critical points: - 3,- 1, 1, 3, ; maimum value: 3; minimum value: 1 B) Critical points: 1, 3; maimum value: -1, 1, 3; minimum value: -, 0, Critical points: -1, 0, 1, ; maimum value: 3; minimum value: 1 D) Critical points: -, -1, 0, 1,, 3; maimum value: 3; minimum value: 1 Identrif the critical points and find the maimum and minimum value on the given interval I. 39) f() = ; I = [-18, 0] Critical points: -18, 0, 9; maimum value 81; minimum value 0 B) Critical points: -9; maimum value 18; minimum value 0 Critical points: -18, -9, 0; maimum value 81; minimum value 0 D) Critical points: -18, 0, 81; minimum value 0 1 0) f(r) = ; I =[-3, 6] r + 39) 0) Critical points: -3, 0, 6; maimum value 1 ; minimum value 1 11 B) Critical points: 0; maimum value 1 ; minimum value 0 Critical points: -3, 0, 6; maimum value 1 ; minimum value 1 38 D) Critical points: -3, 6; maimum value 1 11 ; minimum value 1 38 Using the derivative of f() given below, determine the intervals on which f() is increasing or decreasing. 1) f () = ( - )(8 - ) Decreasing on (-, ); increasing on (8, ) B) Decreasing on (-, ) (8, ); increasing on (, 8) Decreasing on (, 8); increasing on (-, ) (8, ) D) Decreasing on (-, -) (-8, ); increasing on (-, -8) 1) 6

7 ) f () = 1/3( - ) Decreasing on (0, ); increasing on (, ) B) Decreasing on (-, 0) (, ); increasing on (0, ) Increasing on (0, ) D) Decreasing on (0, ); increasing on (-, 0) (, ) ) Find the value or values of c that satisf the equation the function and interval. 3) f() = + 18, [, 9] f(b) - f(a) b - a = f (c) in the conclusion of the Mean Value Theorem for, 9 B) 0, 3-3, 3 D) 3 3) Identrif the critical points and find the maimum and minimum value on the given interval I. ) f() = + ; I = - 3, 1 ) Critical points: 0, ; maimum value 8; minimum value 0 B) Critical points: - 1; minimum value - 1 Critical points: - 3,- 1, 1 ; maimum value ; minimum value - 1 D) Critical points: - 3,- 1, 1 ; maimum value - 3 ; minimum value - 1 7

8 Answer Ke Testname: CAL1-REVIEW 1) C ) B 3) B ) B ) B 6) A 7) C 8) B 9) D ) C 11) D 1) A 13) B 1) C 1) B 16) A 17) D 18) B 19) D 0) D 1) A ) C 3) A ) D ) D 6) A 7) D 8) C 9) D 30) A 31) D 3) D 33) A 3) A 3) B 36) D 37) C 38) D 39) C 0) C 1) C ) D 3) D ) C 8