Examine the function f(x, y) = x^3 - 6xy + y^3 + 7 for relative extrema and saddle points.

The points are "(2,2)".

Step-by-step explanation:

Given value:

Finding the first partial derivation which is equal to 0.

solve both the above equation by equal to 0.

For equation (a)

For equation (b)

by solving the above value in the form of x we get:

by solving the above value in the form of y we get:

Solve the value by applying the second derivation method:

calculating the value of discriminate:

The critical point of the given equation will be (2,2)

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b

let's fu(!

step-by-step explanation: