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Name: __________________________________________ Calculus Derivative Practice 1) Determine the equation of the derivative for each function below and express your answer entirely in terms of positive exponents. f ( x) 3 x 2 g ( x) x3 h( x) 2 x 1 p( x) x r ( x) 6 x 4 5 x 2 3 s ( x) 7 x t ( x) 5 2 5 x3 x2 v( x) 13.2 2) Find when 3) dy = 0, for y 1 x3 4 x 2 12 x . 3 dx f ( x) 2 x 3 find f '(1) 4) f ( x) x n determine the derivative of f(x) with respect to x. 5) If f x 3g x 2h( x) , find the equation for f ' x in terms of g , h, g and h ' x3 1, x 1 6) Let f x 2 , x 1 . x 4, x 1 a) Is f continuous at x = 1. b) Determine the value of the left-hand derivative of f(x) and x=1 c) Determine the value of the right-hand derivative of f(x) and x=1 d) Is f differentiable at x = 1 7) Consider the curve y x 4 4 x3 10 x 2 20 x . 3 Find the x-coordinates of any points where the tangent line to the curve is horizontal. 8) Determine the equation of the line tangent to the graph y x3 4 x at x = 2. 9) Determine the equation of the line normal the graph y x3 4 x at x = 2. 10) f ( x) 2 x 4 5 x 2 Determine f ‘(x) and f ‘’(x). 11) Given f(x) graph f ’(x) 3 f(x) 2 1 -6 -4 -2 2 4 6 -1 -2 -3 f ’(x) 3 2 1 -6 -4 -2 2 4 6 -1 -2 -3 12) Determine the x values when d2y 0 , if y x 4 24 x 2 dx 2 13) g ( x) 3x 2 5 x and g '(a ) 11 . Determine the value of a. 14) Graph a function with the following characteristics a) f ‘ (2) = 0 b) f (x) is differentiable over the real numbers c) f ‘ (x) > 0 when x > 2 3 2 1 -6 -4 -2 2 4 6 -1 -2 -3 15)Graph a function with the following characteristics a) f(x) is continuous at x = 2 b) f(x) is not differentiable at x =2 c) f(x) is neither continous or differentiable at x = -3 3 2 1 -6 -4 -2 2 -1 -2 -3 4 6