Question

To find the global maximum and minimum of a function, you need to take the partial derivatives of the function with respect to x and y, set them equal to zero to find the critical points, and then use the second derivative test to determine whether these points correspond to maxima, minima, or saddle points.

For the function f(x,y)=2x2+7y3+6y2−6x

Answer 1

To find the global maximum and minimum of a function, we need to take the partial derivatives, set them equal to zero to find the critical points, and use the second derivative test. For f(x,y)=2x^2+7y^3+6y^2−6x, we find the partial derivatives ∂f/∂x = 4x - 6 and ∂f/∂y = 21y^2 + 12y.

Step-by-step explanation:

To find the global maximum and minimum of a function, we can follow these steps:

1. Take the partial derivatives of the function with respect to x and y.
2. Set the partial derivatives equal to zero to find the critical points.
3. Use the second derivative test to determine if these points correspond to maxima, minima, or saddle points.

For the function f(x,y)=2x^2+7y^3+6y^2−6x, we need to find the partial derivatives:

∂f/∂x = 4x - 6

∂f/∂y = 21y^2 + 12y

Setting these derivatives equal to zero, we get:

4x - 6 = 0

21y^2 + 12y = 0

Solving these equations will give us the critical points, and then we can use the second derivative test to determine if these points correspond to maximum, minimum, or saddle points.