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- True or False, and explain why showing all steps. The function f (x,y) = x2 + y2 has a global minimum on the disc x2 + y2 < 4.A small aircraft starts its descent from an altitude of 1 mile, 4 miles west of the runway (a) Find the cubic function f(x) = ax3 + bx2 + cx + d on the interval [−4, 0] that describes a smooth glide path for the landing. (b) The function in part (a) models the glide path of the plane. When would the plane be descending at the greatest rate?a.Find the maximum value of w = xyz on the line of intersection of the two planes x + y + z = 40 and x + y - z = 0. b. Give a geometric argument to support your claim that you have found a maximum, and not a minimum, value of w.
- R is the region bounded by y= sqrt x , and y= 6-x and the vertical y-axis. Q is the region bounded by y= sqrt x, and y=6-x, and the horizontal x- axis. (They Intersect at (4,2) ) Label both regions on the graph.Using elimination method, find the minimum distance from the curve y=2-x2 to the origin. f=d2=x2+y2A small aircraft starts its descent from an altitude of h = 6/5 miles, 4 miles west of the runway. a) Find the cubic function f(x) = ax3 + bx2 + cx + d on the interval [−4, 0] that describes a smooth glide path for the landing. b) The function in part (a) models the glide path of the plane. When would the plane be descending at the greatest rate?
- Find the maximum value of f(x, y) = xy subject to y = 3 − x2 Also find the corresponding point (x, y)Fast pls solve this question correctly in 5 min I will give you like for sure. Given f(x,y) = 5x3-3/2y2-15xy, find and label all points in the xy-plane where a saddle point or relative extrema exists.Find the values of a, b, c and d so that the curve f(x)= ax³ + bx² + cx + d has a local maximum at (-2,4) and a point of inflection at the origin.
- Find the absolute maximum and absolute minimum values of f (x , y)=x^2 +y^2 −2x on theregion enclosed by the triangle with vertices (0,−3),(0,3), and (3,0).Check for local maximum and minimum points of the function: f(x, y) = x3 + 3x2y - 3xy - 3x.Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the other two on the positive y-axis and the negative x-axis where the diagonal has length L = 3, occurs when the angles at both (other) vertices are π/4. Include a sketch.