1 Find equations of the tangent line and normal line to the curve at the given point. y = x* + 7ex, (0, 7) tangent line y = normal line y = 2 Find the equation of the tangent line to the curve at the given point. y = 9x - 6Vx, (1, 3) y = Illustrate by graphing the curve and the tangent line on the same screen. A Q 4 N - X 0.5 10 1.5 2.0 0.5 1.0 1.5 2.0 -2.0 -1.5 -1.0 -2.0 -1.5 -1.0 -0.5 O O 3 The equation of motion of a particle is s = to - 27t, where s is in meters and t is in seconds. (Assume t 2 0.) (a) Find the velocity and acceleration as functions of t. v ( t ) = a(t) = (b) Find the acceleration after 7 s. m/s2 (c) Find the acceleration when the velocity is 0. m/$2 4 At what point on the curve y = 2 + 2ex - 5x is the tangent line parallel to the line 5x - y = 6? (x, y) = ( Illustrate by graphing the curve and both lines. -4 -3 -2 -1 1 2 -3 -2 -1 1 2 O O L X -3 -2 -1 2 3 -4 -3 2 O O -6 5 Differentiate. H ( U ) = ( U - vu) ( u + vu ) H ' ( U ) =