Find the relative minimum and maximum

The function has a relative minimum value of f(x,y) = -40 at (x,y) = (2,-5) and no relative maximum.

Step-by-step explanation:

f(x,y) = x² + y² − 4x + 10y − 11

Find the partial derivatives:

∂f/∂x = 2x − 4

∂f/∂y = 2y + 10

Set to 0 and solve:

0 = 2x − 4

0 = 2y + 10

x = 2, y = -5

Evaluate the function at (2,-5):

f(2,-5) = (2)² + (-5)² − 4(2) + 10(-5) − 11

f(2,-5) = 4 + 25 − 8 − 50 − 11

f(2,-5) = -40

Now find the second partial derivative and evaluate at (2,-5):

∂²f/∂x² = 2 > 0

∂²f/∂y² = 2 > 0

The function has a relative minimum value of f(x,y) = -40 at (x,y) = (2,-5) and no relative maximum.

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

341

step-by-step explanation:

all you have to do is 9x31 (which equals 279) and then 20x31 (which equals 620). then you have to subtract. 620-279=341.