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Sketch the graph of the function in Exercise 41

THE ANSWER IS GRAPH

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 4

Limits at Infinity, Infinite Limits and Asymptotes

Derivatives

Missouri State University

Campbell University

Baylor University

Idaho State 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.

01:04

Sketch the graph of the fu…

03:24

So we're asked to sketch the graph of the function. And while we can't actually view the graph of the function, we can understand how we sketch graphs and we understand some important things to look for. So if we have a rational function, the equals P. Of X over Q. Of X where P of X and Q of X are polynomial. Um We know that to find X intercepts, We are going to let p of x equals zero. And those solutions, those solutions that we get will be our X intercepts to find the Y intercepts. We let just X equals zero, will take our zero. And that will tell us are y intercept. Then we can find vertical ascent coats. Once we factor everything thing and cancel it all. We'll find our vertical ascent oats by finding where Q. Of X equals zero. Um And then all of those things combined will help us create our general shape of the graph. We can also pick a couple of points to plot as well.

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