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Sketch a function satisfying the sign diagrams given in Figures 29 a and $29 b$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 3

Concavity and the Second Derivative

Derivatives

Missouri State University

Campbell University

Baylor University

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.

01:05

Sketch the graph of a func…

02:20

Points $A$ and $B$ are giv…

00:24

everybody has to sketch the graph using these sine tables. First thing I said if the first relative we've got going from negative to positive and that indicates that this is going to be a relative, man, okay then we also see that there is a sign change too. This is going to be an inflection point. So this is gonna be helpful here, take a look here at what the sketch would look like here. Then if you got one two, three right now from here we're going increasing and also concave up here, I'm going to do is actually I'm just going to put a hole there and have a good like this that shows from left to right, it's increasing okay. And it's also can't give up you ship operate okay? So then from here we wanted decreasing and concave down. So Decreasing content down looks something like this. But at two switches, two can't give up and then at three it's going to be a relative in and then it will call up afterwards. So that's what possible sketch looks like

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