Suppose That as You Move Away from the Point (-1 $f ( x , y , z )$

question 8

Short Answer

Suppose that as you move away from the point (-1, -1, -1), the function $f ( x , y , z )$ increases most rapidly in the direction $0.6 \vec { i } + 0.8 \vec { j }$ and the rate of increase of f in this direction is 4.At what rate is f increasing as you move away from (-1, -1, -1)in the direction of $\vec { i } + \vec { j } + \vec { k }$ ? Give your answer to 4 decimal places.

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Definitions:

Mean

The average of a set of numbers, calculated by dividing the sum of all values by the total number of values.

Standard Normal Curve

A type of normal distribution that has a mean of 0 and a standard deviation of 1, represented graphically as a bell-shaped curve.

Area

A measure of the extent of a surface or shape, expressed in square units.

Z-score

An indicator that shows the number of standard deviations a particular value is away from the average.