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Temperature readings $ T $ (in $ ^{\circ} $ F) were recorded every two hours from midnight to 2:00 PM in Atlanta on June 4, 2013. The time $ t $ was measured in hours from midnight.

(a) Use the readings to sketch a rough graph of $ T $ as a function of $ t $.(b) Use your graph to estimate the temperature at 9:00 AM

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01:05

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 1

Four Ways to Represent a Function

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

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A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

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In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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all right for this problem. We're going to plot the points which represent the time since midnight and the temperature so of 0 74 Notice I made a break in the graph because, um, it doesn't make sense to go all the way down to zero in this case, and there isn't really room for that. So of 0 74 with 2 70 to 69 we have 4 68 We have 6 66 We have 8 70 We have 10. 78. We have 12. 82 and we have 14. 86. So it kind of make a rough sketch here. And then we can use that to find approximately the temperature at 9 a.m. So 9 a.m. would be right there between eight. And 10. And that would be roughly Oh, maybe 74 75 degrees.

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