3 Consider the function ƒ(x) = 5x³ + 4zº – 10z³ An antiderivative of f(z) is F(x) = Aï” + Bx™ + Cr² + D™² where A is and n is and Bis and mis and Cis
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- For the function f (x) = x4 + 4x3 - 7x2 – 34x- 24 determin a) The intervals of increasing and decreasing b) The location of any maximum and minimum point c) The interval of increasing and decreasing d) The location of any point of inflation.Maximize P = xyz subject to x + z = 12, y + z = 12, x ≥ 0, y ≥ 0, and z ≥ 0Minimize the function 2x1^3+4x1x2^3-10x1x2+x2^2 using powell method. use starting point x^0=[5,2]^T.
- B(3) (a) Find the critical points of the function f(x) = 3x² – 6x. (b) Apply Rolle's theorem for the function f(x) = x² + 4x over the interval [-4, 0]. Justify your answer.Check for local maximum and minimum points of the function: f(x, y) = x3 + 3x2y - 3xy - 3x.f(x,y)= xy2 +(1/6)x3-x+1 function is given.a) Find and classify all critical points of function f.(b) Find the extreme values of the function f under the constraint x2/4+y2=1 by the Lagrange multipliers method.
- Minimize f(x, y) = (2x^2) + (y^2) − xy subject to x + y = 8.Find the maximum and minimum values of the function f(x,y) = 2x^3 + 3y^2 "-4x" - 5 on the domain x^2 + y^2 <= 121Enter the function f(x) = x^2-2x-8 in the form f(x) = a(x-h)^2 + k , where a, h, and k are constants. Enter this function in the first box. Enter the x-coordinate of the minimum value of the function in the second box.