Question: Suppose that a differentiable function f(x,y) has the constant value c along the differentiable curve vec(r)(t)=(:x(t),y(t):); that is,f(x(t),y(t))=cfor all values of t. Show that vec(grad)f

Suppose that a differentiable function f(x,y) has the constant value c along the differentiable curve vec(r)(t)=(:x(t),y(t):); that is,f(x(t),y(t))=cfor all values of t. Show that vec(grad)f is orthogonal to the curve's tangent vector at every point on the curve. Hint: Differentiate with respect to t(5 points)

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