Question

Find the equation for the level curve of the function f(x,y)=4x+4y+1 for the value -1 .

Answer 1

The equation of the level curve for the function f(x,y) = 4x + 4y + 1 when set to the value -1 is found by setting the function equal to -1 and solving for y, resulting in the level curve equation y = -x - 0.5.

Step-by-step explanation:

To find the equation of the level curve for the function f(x,y) = 4x + 4y + 1 at the value -1, we set the function equal to -1 and solve for y in terms of x.

The steps are:

1. Set the function equal to -1: 4x + 4y + 1 = -1.
2. Subtract 1 from both sides: 4x + 4y = -2.
3. Divide by 4 to solve for y: y = -x - 0.5.

So, the equation for the level curve of the function at the value -1 is y = -x - 0.5.