Gradient orthogonal to tangent Suppose that a
Chapter , Problem 8AAE(choose chapter or problem)
Gradient orthogonal to tangent Suppose that a differentiable function \(f(x, y)\) has the constant value c along the differentiable curve \(x=g(t), y=h(t)\); that is,
\(f(g(t), h(t))=c\)
for all values of t. Differentiate both sides of this equation with respect to t to show that \(\nabla f\) is orthogonal to the curve's tangent vector at every point on the curve.
Equation Transcription:
∇
Text Transcription:
f(x, y)
x=g(t), y=h(t)
f(g(t), h(t))=c
nabla f
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