If the curves are far apart it means that the change is rather slow i e it takes a very long distance to nd water that is one degree cooler If the curves are close together it means that the change is rather rapid i e it does not take long to nd water that is one degree cooler Lecture 8 Spacing between level curves The derivative f Linear approximation f Tangent line to f at x What is the derivative It is no one number Partial derivative Change one variable at time Geometrically speaking is the slope of a curve when we intersect slice by plane y c Example Using partial derivative to nd the tangent plane You need a point and the normal vector to that plane To get the normal you must nd two vectors in the plane and cross them Slicing the tangent plane with another plane gives us tangent lines Equation for tangent plane at
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