\fAssume f and g are dierentiable functions with hx}=i{g[x}}. Suppose the equation of the line tangent to the graph at g at the point [2.9] is y = 2:: + 5 and the equation oi the line tangent to the graph pit at (914} is y = 4x 32. a. Calculate h(2} and WE}. b. Determine an equation of the line tangent to the graph of h at the point on the graph where x= 2. The displacement of a mass on a spring suspended from the ceiling is given by the equation shown below. It _ trs 1,rZlile cos [10] a. lGraph the displacement function. h. Compute and graph the velocity of the mess, 1wit]: y']. dy a. Use implicit differentiation to find the derivative dx b. Find the slope of the curve at the given point. sin (y) = 6x - 6; (1,It)dy a. Use implicit differentiation to find the derivative dx b. Find the slope of the curve at the given point. 5xvy + 2y = 28; (2,4)a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to the curve at the given point. sin y + 4x = y"; 4A family of curves forms orthogonal trajectories with another family of curves if each curve in one family is perpendicular to each curve in the other family at each point of intersection. Use implicit differentiation if needed to find dy for each equation of the following pairs. Use the derivatives to explain why the families of curves dx form orthogonal trajectories. y = mx; x 2+y- = a", where m and a are constantsLet h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to compute the following derivatives. a. h'(3) b. p'(1) X 2 w 4 f(x) 1 4 2 f'(x) - 6 - 9 g(x) 08 - N g'(x)