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  2. math.stackexchange.com › questions › 4394100Level curves and critical points - Mathematics Stack Exchange

    Mar 2, 2022 · Let us use the function $f(x,y)=x^3+5 x^2+x y^2-5 y^2$ and check wether it has critical points using level curves. In the first step, let us draw the level curves (blue) and the derivatives $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$ (green).

  3. tutorial.math.lamar.edu › CriticalPointsCalculus I - Critical Points - Pauls Online Math Notes

    Nov 16, 2022 · We say that x = c x = c is a critical point of the function f (x) f (x) if f (c) f (c) exists and if either of the following are true. f ′(c) =0 OR f ′(c) doesn't exist f ′ (c) = 0 OR f ′ (c) doesn't exist. Note that we require that f (c) f (c) exists in order for x = c x = c to actually be a critical point.

  4. math.stackexchange.com › questions › 850011calculus - When are there no critical points? - Mathematics ...

    For example $f(x)=x$ has no critical points. Neither does $f(x)=e^x$. And your function has no critical points, according to many definitions. Some definitions would include endpoints among the critical points. In that case, if we consider the function as having domain $[4,7]$, you have $4$ and $7$. The function is continuous on the interval ...

  5. tutorial.math.lamar.edu › Classes › CalcIIICalculus III - Functions of Several Variables

    Nov 16, 2022 · In this section we will give a quick review of some important topics about functions of several variables. In particular we will discuss finding the domain of a function of several variables as well as level curves, level surfaces and traces.

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  6. activecalculus.org › multi › S-10-7-OptimizationOptimization - Active Calculus

    Find the critical points of the following functions and use the Second Derivative Test to classify the critical points.

  7. www.youtube.com › watchLevel curves and critical points | MIT 18.02SC Multivariable ...

    Level curves and critical pointsInstructor: David JordanView the complete course: http://ocw.mit.edu/18-02SCF10License: Creative Commons BY-NC-SAMore informa...

    • 8 min
    • 45.4K
    • MIT OpenCourseWare

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  9. math.stackexchange.com › questions › 683675calculus - Critical points of a function on a curve ...

    Let $F(x,y) = xy$. Find the critical points of F on the curve $y^2 = x^3 - x$. Thoughts: I'm aware of critical points, however I'm not sure what the question is asking when it means find the critical points of F on the curve. solving: $\nabla F(x,y) = \lambda \nabla H(x,y)$ where $H(x,y) = y^2 - x^3 +x$ I get 3 crit points