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.

a = 3.14

b = 18

c = 18/5 or 3.6 or 3 3/5

step-by-step explanation:

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step-by-step explanation: