Please show solutions.

1. Find the equation of the tangent line to the curve y = f (x) at the given point. a. y - f (x) - x? - x. at (3,6) by = f(x) = 1 x3.at ( 2.9 ) 2. An object moves along a line so that its position at any time t is given by the function s = f(t). where s is measured in meters and t is measured in seconds. Find the instantaneous velocity of the object at the given time t. a. s - f (t) - 12 - 21 + 3, att - 8 3. Differentiate the following using the appropriate theorem on differentiation. a. Find D. (9) b. Find D. (3x ) c. Let / (x) - 2x? and g(x) - 5x. Find DxIf (x) + g(x)]. d. Find Dy (3x* - 5x] + 2). e. Let f(x) - 2x5 and g(x) = 4x?. Find DyIf (x) . g(x)]. f. Let f(x) -3x* + 1 and g(x) = 2x, where g(x) + 0. Find Dx