Please Answer Review Questions

5 7. Let f(x) = ax' + bx' + cx+ 1 . Determine the values of a, b, and c so that f(x) has a point of inflection at x = 2, a local minimum at x = -2, and f(1) = 2. a = b = C = d= 8 . Let {(x) = x* - 4x - 144x" + 3x + 2. a. For what values of x is f(x) concave up? b. For what values of x is f(x) concave down? c. For what value(s) of x does f(x) have a point of inflection? [Hint: construct a table]9 The perimeter of an ellipse is 22. a) Determine the values of a and b that maximize the area of the ellipse. { 2 2 a + b (Hint: The formulas for the perimeter, p. of an ellipse is (approximately) P - 2R 2 , and the area, A. ofan ellipse is A - nab.) a = b = b) What is special about the ellipse of maximum area? 10. An isosceles trapezoid is inscribed in a semicircle of radius 3 cm. Find the angle 9 that will maximize the area of the trapezoid. ABCD 95 the trapezoid. and O is the center of the circle. Write an expression for area of the trapezoid in terms of 9 A(6) = a =