Ünite Sınavı Soruları

A rectangular farming area of 6050 m² needs to be designed. The area is bounded from one side by the wall and requires fencing from the other three parts (one length and two widths). What is the minimum length of the fencing required.

Which of the following is the local minimum point of the function f (x, y) = x² + 2 y² + 2 x + 3 y ?

Which of the following (x,y) point is in the domain of the function  where x and y are real numbers?

z = f(x, y) is defined implicitly by xz + yz - 3 = 0 ; Which of the following ones below is the equation of the tangent plane to the graph of z = f (x, y) around the point (-1, 2, 1) ?

If f(x,y)=3x²y+e^xy+lny

What is the partial derivative ∂²f /∂x² ?

f(x, y) = e^xy + xy² – xy + 2 ; ∂²f / ∂y² = ?

lim_{x→0, y→0} (x² + xy + y²) / (x + xy + y) = ?

z = f(x, y) is defined implicitly by xz + yz – 1 = 0 ; ∂f / ∂x (-1, 2, 1) = ?

If  what is the partial derivative ?

What is the equations of a tangent plane for a function f (x, y) = x²+3y² at a point (x, y) = (1, 1)?

Which of the following is the local minimum point of the function f (x, y) = 3 x² + y² - 2 x - 4 y ?

What is the shortest distance between the point P(0, 2) and the line y = x ?

What is the domain of the function f(x,y)=√(x²-4y²)

How many of the following points are stationary points for the function f(x,y)=x⁴+x²y²-2x²+2y²?

I.(0,0)

II.(1,0)

III.(1,1)

IV. (-1,0)

V.(0,√2)

Given that z=(x+y)², y=u³ x=u²-u find the partial derivative dz/du

What is the value of the limit 

What is the partial derivative f_x of the function f(x, y)=5x²+xy-y²?

Which of the following is the local minimum point of the function f(x,y)=2x²+2xy+2y²-6x ?

z = x² – y ; x = u² v ; y = u² + v² ; at u = v = -1, ∂z / ∂u = ?