3. Partial Derivatives

Directional Derivatives And Gradient — Quiz

Test your understanding of directional derivatives and gradient with 5 practice questions.

Practice Questions

Question 1

What is the definition of the directional derivative of a function $f(x, y)$ at a point $(x_0, y_0)$ in the direction of a unit vector $\mathbf{u} = (u_1, u_2)$?

Question 2

Which of the following best describes the gradient vector $\nabla f(x, y)$ of a function $f(x, y)$?

Question 3

If $f(x, y) = x^2 + y^2$, what is the gradient $\nabla f(x, y)$?

Question 4

In which direction does the function $f(x, y)$ increase most rapidly at a given point?

Question 5

What is the directional derivative of $f(x, y) = 3x + 4y$ at the point $(1, 2)$ in the direction of the unit vector $\mathbf{u} = \left( \frac{3}{5}, \frac{4}{5} \right)$?