Solve the following optimization problem by using Lagrange method: Maximize f(x,x;)=2x, + x, – 3x² -4x +x,x, subject to 0sx, sl and 0Sx, sl.

Please don't provide handwritten solution .....    Fit a quadratic function of the form f(t) = c0 + c1t + c2t to the data points (0,8),(1,7),(2,18),(3,21), usingbleast squares.

Let x be the number of stereos sold with installation and y be the number sold without installation. Weekly revenue collected for these stereos is modelled by; R(x, y) = 300x + 240y – xy – 2² 4 and costs are; C(x, y) = 190x + 130y + 5000 Find the number of installed and uninstalled stereos that will maximize profit. x = y = installed stereos 3y² 8 uninstalled stereos.

Identify which of the following equations are quadratic function or linear function. 1. f(x) = 2x - 5 2. у %3D (х + 1)(х — 6) 3. f (x) — 6х? —7x-5 4. y = 7x + 8 5. y = 9x2 – 16 %3D | Complete the table dtiow of the quadratic function y = x2 – 2x – 3, find the common differences and graph. 1. y = x² – 2x - 3 -2 -1 1 3 4 Transform the following quadratic function into y = a(x – h)² + k. Write the y = x² – 12x + 30 2. f(x) = 2x2 + 8x – 9 → using completing the square → using the formula h and k 1

4. Prove that f(x) = 4x³ – 8x2 + 2x + 1 has three real zeros. %3D