Let f(x, y) = 4x² + 5xy + 2y? – 2x – 3y +1. Find all critical points, and state what type they are.

Q: If 3x = 9y and 27y = 81z, find x/z?

A:

Q: Let t(x) = 2x - 1 and m(x) = x² - X. Find m(t(x)) Be sure to simplify your answer. Use the fx button…

A: Given, t(x) = 2x-1, and m(x) = x2-x m(t(x)) = m(2x-1)

Q: Determine the maximum or minimum value for y = −2(x − 7)(x − 5) and state the value of x for which…

A:

Q: Find two positive numbers x and y that minimize the product xy, and satisfyx + 4y = 120.

A:

Q: The critical points of the function f(x)= 2x-24x+1 are O a. -2,0 O b. 1,2 O c. 0,2 O d. -2,2

A:

Q: Consider the function f(x) = Ax³ + Bx² + 5x. Find the values of A and B if f'(-2) = -3 and f" (-2) =…

A: f(x)=Ax3+Bx2+5x

Q: 2 Suppose y is a function of x such that y * and y(4) = -3. Find y. |

A: The differential equation is given by y' = 2x                                   .......(1) Initial…

Q: e-X f(x, у) %3D x2 + y2

A:

Q: 1 √x y³+1 2 Sőt. S²/E 0 dydx

A: We are given an integral. Our aim is to evaluate the integral ∫04∫x21y3+1dydx.

Q: Compute f 3 2 x-5x+6 dx.

A:

Q: f(x) = /x2 + 1 x²

A: Find the domain

Q: 2x-3 5. Let f(x) = find 3x+4 Ax as Ax -0

A:

Q: The domain of function x) = In(2– x) is %3D

A:

Q: Find fxxx for f(x,y)=x2y2

A:

Q: The function v= xex is a particular solution of y' + 2y – 3y= 4e*.

A: To check if  y = x ex is  particular solution of y'' + 2y' - 3y = 4 ex

Q: Solve for the values of Ay and dy if y= f(x) =x² + 2x? – 3x + 5 and x changes from 2 to 2.10.

A: Given: y=fx=x3+2x2-3x+5 And x1=2 &  x2=2.10  a). We know that; ∆y=yx2-yx1 So,…