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

Determine the number of real roots of the equation $x^{3}+3 x^{2}-9 x-15=0$

$$3$$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 3

Concavity and the Second Derivative

Derivatives

Oregon State University

University of Michigan - Ann Arbor

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.

01:42

Find the real roots of the…

00:51

00:47

Solve each equation. State…

$x^{3}-15 x+1=0 \quad$ (th…

01:08

01:05

Use a calculator to solve …

we want to determine the real roots of the function X cubed plus two, X squared minus nine X minus 15 is equal to zero. To solve this problem, I recommend using a graphing calculator such as demos for which I've already included. A screenshot on the lower left corner. A graphing calculator such as does most will graph for you the function overall X. And then we'll also tell you when you zoom in on these great points marked as zeros exactly what the X values of the zeros are. The X values of the zeros are of course the roots. So we're deploying graphic graphic calculator solved. So just note that recommendation. You can also use a route solver online. There are numerous route solvers that don't require graphing calculator but with a root solver. Dual graphing calculator like DEz most. You can find the roots easily from this. You find that the roots are the following X equals negative 3.35 X equals negative 1.546 and X equals 2.896

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:27

Sketch the graph of the function defined by the given equation.$$y=f(x)=…

02:57

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

01:10

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

00:50

Determine the equation of the inverse function.$$f(x)=5 x-9$$

01:39

01:44

While we have stated the chain rule, for the most part we examined the speci…

01:29

Determine where the function is concave upward and downward, and list all in…

03:24

An alternative way to do implicit differentiation is to introduce a mythical…

01:37

Determine if the equation describes an increasing or decreasing function or …

03:32