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A homeowner mows the lawn every Wednesday afternoon. Sketch a rough graph of the height of the grass as a function of time over the course of a four-week period.

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The height of the grass is always the same height on each day. The height increases linearly startingfrom a minimum on Wednesday, and returning to that minimum the next Wednesday.

01:03

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

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

04:31

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.

12:15

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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okay, We're going to draw a simple graph that represents the height of the grass, and the grass is cut every Wednesday over the course of a four week period. And, of course, there are a lot of things that could change in different amounts of rain and sun and fertilizer. But we're just going to ignore all of those periphery details that we don't know and just imagine that the grass is growing at a steady rate all week until it's cut on Wednesday. And then it's growing at the steady rate again until it's cut the next Wednesday and so on and so on just comes back down suddenly to that cut length every Wednesday.

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