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Sketch the graph of a continuous function increasing on $-1<x<2$ and decreasing on $2<x<4$. Indicate the point $M$ on your graph which is a relative maximum.

ANSWER IS GRAPH

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 1

Extrema of a Function

Derivatives

Missouri State University

Campbell University

Harvey Mudd College

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

01:20

Sketch the graph of a cont…

01:49

Graph the piecewise-define…

Graph the function. Estima…

02:07

01:56

02:26

Sketch a graph of $f(x)=\f…

02:23

Yeah. This exercise asks us to draw a graph of continuous function that is increasing on -1- two and decreasing on 2- four. There are many choices. But here I just use a quadratic function. This quadratic function is F X equals miners, tax miners to square. Since this function is increasing to the left of X equals two and decreasing to its right, its maximum is at X equals two. No, here's a black curve is a graph of this function and the right night is a derivative of this function. It's derivative. Yes. Have primaries because minus two X. Platform, The derivative is positive to the left of the X equals two and negative to its rights enhancing equals zero at X equals two. That is also the relative maximum of this function.

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