Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Sketch the graph of the function defined in the given exercise. Use all the information obtained from the first derivative.Exercise 24.

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 2

The First Derivative Test

Derivatives

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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.

00:47

Sketch the graph of the fu…

01:00

01:01

00:52

01:04

01:20

03:43

05:47

02:56

01:34

Sketch the graphs of the g…

02:05

01:55

Information We found out and exercise 24, we have our minimum maximum and inflection point. So to plot this on a graph, First we have 10, Then we have negative 30 and -97, which is about here and then 137 will make way up there. So since on either side we found out that it was positive and positive at the inflection point we know that this is going up. And then for the maximum we have that's a very bad inflection point. Let me redraw that. Okay. And then for a maximum we have positive going up negative coming down and then that are negative. We have negative or negative going one way and then a positive are increasing going the other way. So this is what our graph will look like. Remember this is all approximate based on what are derivative gave us

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:33

Determine the extrema of the function defined by the equation $f(x)=\frac{x}…

04:33

Consider the function given by$$f(x)=\left\{\begin{aligned}x+3 &…

01:12

Determine whether or not the function determined by the given equation is on…

03:03

Sketch the graph of the line $x-2 y+1=0$ on the same axes as the graph of $y…

Use linearization to approximate the given quantity. In each case determine …

00:57

$$\text { Find } f^{\prime \prime}(x) \text { if: (a) } f(x)=x^{5}+3 x^{2}+5…

05:48

(a) Find $d$ fif $f(x)=\frac{2 x+3}{x^{2}-2}$,(b) Find $d y$ if $y=\frac…

01:21

Use the first and second derivatives to sketch the graph of the given equati…

$$\text { Find } \frac{d^{2} y}{d x^{2}}, \text { if } x^{1 / 2}-y^{1 / 2}=6…

03:04

(a) Find the $x$ -intercept(s); (b) Find the vertical asymptotes; (c) Find t…