Subjects multivariable calculus

Plane 2X2

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

Plane 2X2


1. **State the problem:** We have a function of two variables: $$u(x_1, x_2) = 2 x_2$$. 2. **Analyze the function:** The function depends only on $$x_2$$ and is linear in $$x_2$$ with slope 2. There is no dependence on $$x_1$$, so the surface will be constant along the $$x_1$$ axis. 3. **Graph interpretation:** Because $$u$$ varies linearly with $$x_2$$ and is constant with $$x_1$$, the graph is a plane parallel to the $$x_1$$ axis. 4. **Summary:** The shape is a plane rising linearly in the $$x_2$$ direction at twice the rate: $$u = 2 x_2$$. This matches the description of a flat plane anchored at the origin extending upward with no $$x_1$$ dependence.