3. Partial Derivatives

Tangent Planes And Linearization — Quiz

Test your understanding of tangent planes and linearization with 5 practice questions.

Practice Questions

Question 1

What is the general form of the equation of a tangent plane to a surface defined by a function $z = f(x, y)$ at a point $(x_0, y_0)$?

Question 2

If $f(x, y) = x^2 + y^2$, what is the equation of the tangent plane at the point $(1, 2)$?

Question 3

Which of the following best describes the concept of linearization of a function $f(x, y)$ at a point $(a, b)$?

Question 4

Consider the function $f(x, y) = 3x - 2y + 7$. What is the tangent plane at the point $(1, 1)$?

Question 5

For the function $f(x, y) = x^3 + y^3$, what is the linear approximation at the point $(1, 1)$?