Critical Points and Function Values Quiz

What are the critical points where the function has absolute maxima?

• (1, 0) and (-1, 0)

• (0, 1) and (0, -1)

• (1, 1) and (-1, -1)

• (0, 0) and (1, 1)

What is the value of the function f at the critical point (1, 0)?

• 0

• 1

• 2

• -1

Which critical points correspond to absolute minima?

• (0, 1) and (0, -1)

• (1, 0) and (-1, 0)

• (1, 1) and (-1, -1)

• (0, 0) and (1, 1)

What method is suggested to redo Exercise 14.7.4 in Exercise 14.8.2?

• Integration by parts

• Lagrange multipliers

• Partial fraction decomposition

• Substitution method

What is the equation of the plane mentioned in the exercise?

• x + y + z = 4

• x + 2y + z = 4

• 2x + y + z = 4

• x + y + 2z = 4

What is the point from which the shortest distance to the plane is to be found?

• (1, 0, 2)

• (1, 0, -2)

• (0, 1, -2)

• (1, 2, 0)

What is the function \( g(x, y, z) \) given in the image?

• \( x + y + z = 4 \)

• \( x + 2y + z = 4 \)

• \( 2x + y + z = 4 \)

• \( x + y + 2z = 4 \)

What is the gradient of \( g \), \( \nabla g \), as shown in the image?

• \( \langle 2, 1, 2 \rangle \)

• \( \langle 1, 2, 1 \rangle \)

• \( \langle 1, 1, 1 \rangle \)

• \( \langle 2, 2, 2 \rangle \)

According to the image, what is the expression for \( \nabla f \)?

• \( \langle 2(x+1), 2y, 2(z+2) \rangle \)

• \( \langle 2(x-1), 2y, 2(z+2) \rangle \)

• \( \langle 2(x-1), y, 2(z+2) \rangle \)

• \( \langle 2(x-1), 2y, z+2 \rangle \)