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Lecture 11

# MAT 211 Lecture 11: 15.1 Functions with Several Variables & 15.2 Partial Derivatives Premium

4 Pages
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Department
Mathematics
Course Code
MAT 211
Professor
Mohacsy Hedvig

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Description
15.1 Functions with Several Variables Function with a single variable is a rule that assigns a one unique output for every input Linear function: • m is slow, the constant rate of change Deﬁnition: a real valued function f of x, y, z is a rule that assigns a unique output value for each sequence of inputs x, y, z.... Ex. Ex. Function with two variables Linear function with two variables Ex. • 2 is the slope in the x direction • -3 is the slope in the y direction • The rate of change of z with respect to x (y is ﬁxed) is 2 (the slope in the direction of x) ◦ 1 unit increase in x (y is ﬁxed) results in 2 unit increase in z • The rate of change of z with respect to y (x is ﬁxed) is -3 (the slope in the direction of y) ◦ 1 unit increase in y (x is ﬁxed) results in a 3 unit decrease in z Ex. Brand Z's annual sales are aﬀected by the sales of related products X and Y as follows: each \$1 million increase in sales brand X causes a \$2.7 million decline in sales of brand Z, whereas each \$1 million increase in sale of brand Y results increase of \$0.7 million in sales of brand Z. Currently, brands X, Y, Z are each selling \$6 million per year. Model sales of brand Z using a linear function (in millions of dollars). A lin
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