# Multi-Calculus 3 Question Level curves

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 $t$

• You mean $\nabla f$ not $\Delta f$? – Jacky Chong Apr 7 '17 at 1:36
• Yes, thanks you! – fireshock Apr 7 '17 at 1:38
• Differentiate both sides – qbert Apr 7 '17 at 1:55