17.) For the equation y2 + 2xy + x2 = 16 find the slope of the tangent line at the point (1,3). A. 5/7 B) 2/3 C) 4 D) 3 E )- 1 18.) Given cos(x+y)= x2 + 1 use implicit differentiation to solve for dy/dx. 19.) For the following function solve for dy/dx y = 54x A) 5 (In 4) 54x B) 4 (In 5) 54x C) 20 (In 5) 54x D) 20 (In 4) 54x 20.) If log4 x2 determine the value of f '(X) A. 2x4 B) 4x C) 2/xlog4 D) 2x/10g4 21.) If g(x)=arctan(2x-1) determine the value of f(3) A. 113 B). 21+(2x-1)2 C. 237 D. 7429.) Below is a chart describing the values of a function fand its derivatives at various points. If the function is continuous and differentiable, which of the following statements must be true: A) (1, 14) is a relative minimum B) (3. 19) is a possible point of inection C) (4, 21) is a relative maximum D) All of the above must be tme E) None of the above must be true 30.) Let f(x) = x + 2 sin 1:. Determine the exact xvalue(s) where a relative minimum occurs on the interval from [0, 2pi] 31.) You are filling up a cylindrical glass with lemonade. The radius of the glass is 1.5 inches. You are filling the glass at a rate of 2 cubic inches per second. What is the rate of change of the height of the lemonade in the glass? 32.) You are working forJPL and are landing a rover on Mars. The landing will create a circular crater, as the rover lands, the circular crater's radius will expand at a rate of 12 meters per second. Find the rate of change of the area of the circular crater when the radius is 20 meters. 27.) f(x) = x2 - 6x + 12 MVT/Rolle's Theorem 2 Let f(x) represent the graph above. Which of the following points satisfies the MVT (mean value theorem) for the function f(x) on the interval [0, 6]. A) X=0 B) X=2 C) X=3 D) X=5 E) The Mean Value Theorem Does Not Apply 28.) Let f be the function given by f (x) = -2x3 + 6x2. The graph of f is concave up when (A) x > 1 (B) x 2 only (E) x