Question: please help with the questions below Name Date Unit 2 MC Problems - Unit 2 Review Problems AP Calculus Directions: Show all work or explain

please help with the questions below

please help with the questions below Name Dateplease help with the questions below Name Dateplease help with the questions below Name Date
Name Date Unit 2 MC Problems - Unit 2 Review Problems AP Calculus Directions: Show all work or explain where appropriate and select the best answer, 1) If h(x) is a function which of the following is the definition of the derivative at x = Q? a) lim f( x+a)-f(a) ha h b) lim Lath)-f(a) h -+0 h C) lim I(x)-f(a) x - a x - a d) Band C e) None of the above 2) The tangent line to the curve y = 2x2 - 3x, with y' = 4x - 3, will be horizontal when x=? a) x =0 b) x =2 C) x = 3/4 d) x = 4/3 x - a 3) If g is such a function that lim = 5 which of the following must be true? x - a a) fla) = 5 b) fla) does not exist c) f(x) is continuous at x = 5 d) f'(a ) = 5 e) a = 5 4) If f(x) = -12 + x, then which of the following expressions represents f'(a) ? A) lim ( -x2 + x th) - (-22+2) B) lim ( -a2+ath) - (-12+ 1) c) [-(2+ h)2 + (z + h)] -(-22+) D) lim I-(3 + h)2 + (x + h)] - (-22+2) h E) None of these5) The limit below expresses the derivative of a function. Which of the following functions describes the original function? lim [5(x + h)2-41-[5x2 -4] h a) f (x) = 5(x + h) 2 - 4 b ) f ( x ) = - 5 (x + h ) 2+ 4 c) f(x) = 5x2-4 d) f(x) =-5x2 +4 e) f (x) = 5x2 6) The limit below expresses the derivative of a function. Which of the following functions describes the original function? 3 ( x + h ) 2 - (x + h ) - 4- 3x2 + x+4 h - 0 h a) f(x) = 3(x + h)2 - (x+h)-4 b ) f ( x ) = - 3 ( x + h ) 2 + ( x + h ) + 4 c) f(x) = -3x2 + x+4 d) f(x) = 3x2 - x-4 e) f(x) = 312 -x 7) If the function f(t) describes the number of miles that you travel t hours after the starting point, then what would be the units of f'(t)? a) miles b) miles/hour c) hour/mile d) mile e) hours 8) If the function f(t) describes the number of bags on a plane t hours after takeoff, then what would be the appropriate units of f' (t) ? a) b ) bags /hour c) hour/ bags d) bags e) hours 9) The function f(x) has a point f(3) = 2 and f'(3) = 7. Use the tangent line to f(x) at x = 3 to approximate the value of f(4). a) f ( 1 ) = 2 b) s( 1 ) = 3 c) 1( 4 ) = 9d) f (4) = 12 e) f(4) = 17 10) The function f(x) has a point f(1) = 4 and lim )= 5 . Use the tangent line to f (x) at x = 1 to approximate the value of f (2). x -1 x - 1 a) f(2) = 1 b ) f ( 2 ) = 4 c) f ( 2 ) = 5 d) f ( 2 ) = 9 e) f(2) = 15 11) The tangent line to the curve y = 5 -15 3x+5' with y' = - (3x+5)2, will be horizontal when x=? a) x = 1 b) x =-5 C) x = 5 d) x = 5/3 e) no such x value exists 12) The tangent line to the curve y = v3x - 5, with y' =: 1 2V/3x-5 , will be vertical when x=? a) x =1 b) x = 2 C) X = 3/5 d) x = 5/3 e) no such x value exists

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