please help with the questions below

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