7. Optimization with Constraint Find the minimum of Q=x² + y²if x+y = 6.
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- How are the absolute maximum and minimum similar to and different from the local extrema?5.Find the maximum of Q=xy if x+y=42. The maximum value of Q is Q=?What values of a and b make ƒ(x) = x3 + ax2 + bx have a. a local maximum at x = -1 and a local minimum at x = 3? b. a local minimum at x = 4 and a point of inflection at x = 1?
- Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 4 at x = −4 and a local minimum value of 0 at x = 2.How to find the the relative maximum or minmum of the function: e^(3x^2+4) with x and y coordinatesFind the values of constants a, b, and c so that the graph ofy = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection point at (1, 11)
- A manufacturer determines that the profit P (in dollars) obtained by producing and selling x units of Product 1 and y units of Product 2 is approximated by the model P(x, y) = 8x + 10y − (0.001)(x2 + xy + y2) − 10,000. Find the production level that produces a maximum profit. What is the maximum profit?Minimize g=10x+9y Subject to 4x+y≥19 2x+y≥13 x+4y≥24 x≥0 y≥0 What is the minimum value and at which point?4.Consider the functionf(x,y)=−x2−y2+6x+2y a.Find the values of x∧y that correspond to the stationary point(s) of this function. b.Determine whether the point(s) you identified in part (a) is a maximum, a minimum, or neither