Find the maximum rate of change of f at the given point and the direction in which it occurs....
Question:
Find the maximum rate of change of {eq}f {/eq} at the given point and the direction in which it occurs. {eq}f(x, y, z) = \frac{x + y}{z}, \quad (1, 1, -1) {/eq}
Maximum Rate of Change:
The maximum rate of change of the function is represented by the modulus of the gradient of the function evaluated at the specified point expressed in the form as {eq}\left| {\nabla f\left( {x,y,z} \right)} \right| = \sqrt {{a^2} + {b^2} + {c^2}} {/eq}, where {eq}f\left( {x,y,z} \right) {/eq} is the function with three variables, {eq}\left( {x,y,z} \right) {/eq} is the specified point, and {eq}\nabla f\left( {x,y,z} \right) = \left( {a,b,c} \right) {/eq}.
Answer and Explanation: 1
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Given:
- Consider the function {eq}f\left( {x,y,z} \right) = \dfrac{{x + y}}{z} {/eq} and the point {eq}\left( {1,1, - 1} \right) {/eq}.
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Determine the Rate of Change of a Function
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Chapter 4 / Lesson 4
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The rate of change of a function can refer to how quickly it increases or that it maintains a constant speed. Learn the definitions of linear rates of change and exponential rates of change and how to identify the two types of functions on a graph.
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