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AP Calculus Practice (3.1-3.3) For each of the following functions, find the derivative. For each derivative, determine all values for which the derivative does not exist. For each of these values determine if the derivative does not exist due to a discontinuity, a corner point, a cusp, or a vertical tangent line. 1 ) f ( x ) = 3x 3 x +1 2) f (x ) = 4x (3x' - 1 ) 3) f (x ) = 2x + 3 4) f (x) = 2x ( 5x' + 1) 5) f ( x ) = - x' +1 6) f(x)= 3x' (4x2 +3) Find the equation of the tangent line to the graph of the given function at the given point. 7) f ( x ) = Vx' +- -2 at x=1 8) 8 (x ) =- 2x x' + 2 at x = 2 Find the equation of the normal line to the graph of the given function at the given point. 9 ) f ( x ) = Vx' - -5 at x=-1 10) g (x) = x (3x* +1) at x =1