6 Calculus 101 Questions

1.

Consider the parabola y = 6x x2. (a) Find the slope of the tangent line to the parabola at the point {1, 5). (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. Y Y Find an equation of the tangent line to the curve at the given point. y: v'}. (1,1) Find an equation of the tangent line to the graph of y = g(x) at x = 2 if 9(2) = 4 and g'{2) = 5. {Enter your answer as an equation in terms of y and x.) E If the tangent line to y = f(x) at (3, 2) passes through the point (0, 1), find f(3) and f'(3). f (3 ) f'(3) =The limit represents the derivative of some function fat some number a. State such an f and a. lim (1 + h ) 4 - 1 h - 0 h Of (x) = x4 - x, a=1 Of ( x ) = x# 4 +x, a=0 Of ( x) = x4, a=1 Of ( x ) = x, a=0 Of ( x) = x, a = 2If a ball is thrown into the air with a velocity of 38 Ft/s, its height (in feet) after t seconds is given by y : 38f 16:2. Find the velocity when t : 1. ft/s