Solve the following Differentiation: Composite, Implicit, and Inverse Functions: References and topics to know:

	03.01 The Chain Rule Segment: 1
	03.02 Implicit Differentiation Segment: 1
	03.03 Differentiating Inverse Functions Segment: 1
	03.05 Differentiating Inverse Trigonometric Functions Segment: 1
	03.06 Selecting Procedures for Calculating Derivatives Segment: 1
	03.07 Calculating Higher-Order Derivatives Segment: 1

Question 1 (Essay Worth 30 points) (03.01 HC) x f ( x) f'( x) g(x) g'( x) 2 4 2 3 1 3 -1 -5 4 4 2 5 4. 5 6 2 3 -1 The functions f and g have continuous derivatives. The table gives values of f, f', g, and g' at selected values of x. Part A: Find h'(2) if h(x) = g(f(x)). (5 points) Part B: Find m'(2) if m(x) = f(x2). (5 points) Part C: Let k(x) = f(g(x)). Write an equation for the line tangent to the graph of k at x = 3. (10 points) f ( x ) Part D: Let j(x) = 90. Find j'(2). (10 points)Question 2 (Essay Worth 30 points) (03.02 HC) A graph is defined by the equation 3y(4 - x) = x. Part A: Find %_ (10 points) Part B: Find the equation of the tangent and normal line at the point (6, 1). (10 points) Part 0: Find the x- or yvalue of each point where the slope of the original equation is undened. (10 points) Question 3 (Essay Worth 40 points) (03.07 HC) A curve is represented by the equation 23 + xy - 6x + 3 = 0. Part A: Determine y (10 points) Part B: Evaluate y at the point (1, 1). (10 points) dx Part C: Determine _y (10 points) dx 2 Part D: Evaluate y at the point (1, 1). (10 points) x 2