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Figure 2 is a graph of the level curves of this function corresponding to [latex]c=0,\ 1,\ 2[/latex], and [latex]3[/latex]. Note that in the previous derivation it may be possible that we introduced extra solutions by squaring both sides. This is not the case here because the range of the square root function is nonnegative.
The Gradient and Level Curves Given a function . f. differentiable at (a, b), the line tangent to the level curve of . f. at (a, b) is orthogonal to the gradient .
Learn how to find level curves of a function in Calculus 3.
- 13 min
- 74K
- The Math Sorcerer
Feb 28, 2021 · Calculus 3 video that explains level curves of functions of two variables and how to construct a contour map with level curves. We begin by introducing a ty...
- 21 min
- 22K
- Houston Math Prep
Aug 17, 2017 · We discuss level curves: what are they, how do you find them, and what do they look like?
- 12 min
- 18.4K
- Catherine Schmurr
Aug 17, 2024 · For the function \(f(x,y)=x^2−2xy+5y^2+3x−2y+3\), find the tangent to the level curve at point \((1,1)\). Draw the graph of the level curve corresponding to \(f(x,y)=8\) and draw \(\vecs ∇f(1,1)\) and a tangent vector. Hint. Calculate the gradient at point \((1,1)\). Answer
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Recall also that the gradient \(\nabla f\) is orthogonal to the level curves of \(f\) This page titled 3.5: Level Curves is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jeremy Orloff ( MIT OpenCourseWare ) via source content that was edited to the style and standards of the LibreTexts platform.
