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Powerpoint Jeopardy Definition of Basic Equation of Product & Chain Rule Derivatives Derivatives Tangent Line Quotient Rule 10 10 10 10 10 20 20 20 20 20 30 30 30 30 30 40 40 40 40 40 50 50 50 50 50 Use the definition of derivatives to find the slope of the graph of f ( x) 2 x 3 at the point (2, 1). Use the definition of a derivative to calculate the derivative of f ( x) x x 2 Is the function f(x)=|x – 2| differentiable everywhere? If not, why not? Use the definition of derivatives to find the derivative of 2 y t Insert Text for Questio Category 1 – 50 points (a) Is the slope of the tangent line at (-3, -3) positive, negative or zero? (b) Is the slope of the tangent line at -1 positive, negative or zero? Find the derivative of x-9 Let g ( x) 5 f ( x) and let f '(7) 6. Find g '(7). Suppose the position equation for a moving object is given by s (t ) 3t 2t 5 2 where s is measured in meters and t is measured in seconds. Find the velocity of the object when t = 2. The volume of a right circular cone of radius r and height r is given by V r 3. 3 How fast is the volume changing with respect to changes in r when the radius r is equal to 2 feet? The graph below represents the graph of the derivative of what function? Find an equation of the tangent line to the graph of the function f(x) = 2 sin x at the point where x 3 Find an equation of the tangent line to the graph of f ( x) 2 x 2 2 x 3 at the point where x = 1. Find an equation of the tangent line to the graph of f(x) = tan x at the point ,1 . 4 Find an equation for the tangent line to the graph of f ( x) x 1 at the point where x 3. Find an equation for the tangent line to the graph of f ( x) 2 x 1 at the point (4,3). Differentiate: f ( x) x tan x. csc x Find y’’ for y . 2 Let f(3) = 0, f’(3) = 6, g(3) = 1 and g’(3) = 1/3. Find h’(3) if h(x) = f(x)/g(x). dy Find for y x (3x 1). dx Differentiate: 1 cos x y . 1 cos x Find the value of the derivative of f ( x) 2( x 3) at the point (2, 2). 2 Find the derivative of f ( x) x 1 2 2 Find the derivative of y tan x 4 x 1 Find the derivative of y x Evaluate the derivative of 1 2 y cos x at the point , . x 2