1. (03.01 MC) Given f(x) = tan-(4x2), then f'(x) is equal to which of the following? (6 points) 16xsec2(4x2)tan(4x2) O 2sec2(4x 2) O tan2(8x) O 16xsec2(4x2) 2. (03.02 MC) dx What is % of x = tan(y)? (6 points) O sec2(v) O sin(y) O cot(y) Ocos2(v) 3. (03.02 HC) A graph is defined by the equation x2 - v2xy+3y? =23. Part A: Find . (5 points) dx Part B: Find the equation of the tangent line and the normal line at the point (v2,3). (5 points)4. (03.03 MC) It is known that function f is an increasing function that satisfies f(-1) = 4 and f'(-1) = 2. Use this information to compute f-1(4). (6 points) O -1 O 4 O NI - 5. (03.03 HC) No calculator is allowed for this question. A function h is dependent on x and is differentiable for all real numbers. Let k be the inverse of h. Part A: Use the derivative of the inverse functions rule to write an expression for k' in terms of k, h, and x. (7 points) Part B: Use the table of values to find k'(1). (3 points). X 1 2 3 h(x) -4 0 1 h'(x) 0 16. (03.03 HC) Let k be a decreasing function such that k(_) = -> and k'(x) = -2x2 + 3. If g is the inverse of k, which of the following is equal to g'(->)? (6 points) 1 WIN | - O CIN 7. (03.01 MC) The table gives values of f, f ', g, and g' at selected values of x. If h(x) = f(g(x)), then h '(5) is equal to which of the following? (6 points) x f(x) f' (x) g(x) g'(x) 2 1 7 3 5 -3 2 5 5 -2 9 O -4 O 8 O -7