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- Find the maximum area of a rectangle in the first quadrant where one side of the rectangle lies along the line y = 10 – 2x and where the two vertices which are not on the given line are on the positive x- and y- axes.Q1: Locate the zeros of the following functions and determine their order. 1) z4+ 10z²+9.; 2) z³ exp(z-1). 02. Locate the singularities of the following fFind the exact global maximum and minimum values of the function. f) = 4x – 4lnx for x> 0 If there is no global minimum or maximum enter "NA". The global minimum is The global maximum is
- Find the values of constants a, b, and c such that the graph of y = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection point at (1, 11).2. Sketch the curve y = x³ 3x² in the region -2 5x 55. Find raph. .Sketch the graph y = mon!! x² (2-x). Find the local maximum, minimum and points of inflection.Q.1 A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 -16x3-24x2 + 37 is
- Determine the interval(s) over which the graph of y=x4-4x³ +7 is concave up or concave down. a.) Concave up on (3,0) Concave down on (-∞,3)U(0,3) b.) Concave up on (-∞,2) U (2,00) c.) Concave up on (0,2) Concave down on (-∞,0)U(2,00) d.) Concave up on (-∞,0) U (2,∞) Concave down on (0,2)11) Find each of the two areas bounded by the curves y = x3-4x and y = x² + 2x. Points of intersection: (0, 0), (3, 15) and (-2, 0) (-2, 0) (-1.15, 3.08) A da (-1,-1) (3, 15) (1.15,-3.08)Find the absolute maxima and minima of the function on the given domain. (x y) = 2x2 + 9y2 on the disk bounded by the circle x2 + y? = 9 O A. Absolute maximum: 81 at (0, 3) and (0, –3); absolute minimum: 0 at (0, 0) O B. Absolute maximum: 99 at (3, 3); absolute minimum: 0 at (0, 0) O C. Absolute maximum: 18 at (3, 0) and (-3, 0); absolute minimum: 0 at (0, 0) O D. Absolute maximum: 81 at (0, 3) and (0, -3); absolute minimum: 18 at (3, 0) and (-3, 0)