A path in $juniorg8.combb R^2$ is a continuous attribute $phi : o juniorg8.combb R^2$. Finding maxima and minima of a duty $f$ along a route $phi$ indicates finding maxima and also minima of the attribute $f circ phi$.
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For instance if $f(x, y) = xy$ and also $phi(t) = (cos(t), sin(t))$, with $t in <0, 2 pi>$, then to discover the maxima and minima of $f$ along $phi$ (the unit circle) you would discover the maxima and minima of $$(f circ phi)(t) = cos(t) sin(t), qquad t in <0, 2pi>$$
I understand tbelow are maximums and also minimums as soon as the derivative of a function is equal to 0
This is not true, take into consideration $f(x) = x^3$ at $x = 0$. What is true is that if $f$ is differentiable at $x_0$ and $x_0$ is a regional extremum then $f"(x_0) = 0$
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