Solve the following problems involving Chain Rule and Implicit Differentiation. 1. Find the slope and the equation of the tangent line to the graph of g(x) = 5 at x = (x-4) -1. 2. Sheryl deposited Php50,000.00 in an account with an annual interest rate of r compounded annually. At the end of ten years, her balance is given by the function A = 50, 000(1 + r) . What is the rate of change when r = 0.06? 3. Consider the conic section with the equation 16x + 9y"- 32x + 36y - 92 = 0 a. What kind of conic section is the given equation? b. Sketch the graph of the equation using graphing software. c. Find the slope of the tangent line to the curve at (3, 1). d. Determine the equation of the tangent line to the curve at (-1, 1) 4. Lara and Shella both start from point A and drive along perpendicular roads AB and AC S respectively as shown in the figure. Lara drives at a speed of 45km/hour and Shella travels at a speed of 40km/hr. If Shella begins one hour before Lara at what rate are their cars separating three hours after Shella leaves. Note. All variables are changing with time, x = x(t), y = y(t), and r = r(t) given implicitly