4. Statistics

Correlation Regression — Quiz

Test your understanding of correlation regression with 5 practice questions.

Practice Questions

Question 1

Using Lagrange multipliers, find the maximum value of $f(x,y,z)=xyz$ subject to $x+y+z=6$ with $x,y,z>0$.

Question 2

For $f(x,y)=x^4-4x^2+y^4-4y^2$, classify the critical point at $(0,0)$.

Question 3

Compute the directional derivative of $f(x,y,z)=x^2e^{yz}+yz$ at $(1,0,1)$ in the direction of $(2,-1,2)$.

Question 4

Find the equation of the tangent plane to the surface $z=\ln(xy)$ at $(1,2,\ln2)$.

Question 5

Evaluate $\int_{0}^{1}\int_{x^2}^{\sqrt{x}}xy\,dy\,dx$ by reversing the order of integration.