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I don't know how to start this problem? Any hints? I don't even think I know what it is saying....

Let $f(x,y)$ be a differentiable function, $f: \mathbb{R}^2 \rightarrow \mathbb{R}$. Suppose $f$ has a smooth level curve $f(x,y)=c$, parametrized by the path $r(t) = <x(t),y(t)>$, $t \in \mathbb{R}$. Show that $\nabla f $ satisfies: $\nabla f$ is orthogonal $r'(t)$ at every $t$

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  • $\begingroup$ You mean $\nabla f$ not $\Delta f$? $\endgroup$
    – Jacky Chong
    Apr 7, 2017 at 1:36
  • $\begingroup$ Yes, thanks you! $\endgroup$
    – fireshock
    Apr 7, 2017 at 1:38
  • $\begingroup$ Differentiate both sides $\endgroup$
    – operatorerror
    Apr 7, 2017 at 1:55

1 Answer 1

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Hint: Use chain rule to compute \begin{align} \frac{d}{dt}f(x(t), y(t))= \frac{d}{dt} c \end{align}

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