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# Rate of change

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Suppose that the temperature at the point (x, y, z) in space (in degrees Celsius) is given by the formula: W= 100 - x^2 - y^2 - z^2. The units in space are meters. (a) Find the rate of change of temperature at the point P(3, -4, 5) in the direction of the vector v=3i - 4j + 12k. (b) In what direction does W increase most rapidly at P? What is the value of the maximal directional derivative at P?

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This solution shows how to find the rate of change of temperature at a given point.

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(a) Gradient of W =dW/dx(i)+dW/dy(j)+dW/dz(k), where (i),(j) and (k) are unit ...

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