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Is there a number that is exactly 1 more than its cube?

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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 5

Continuity

Limits

Derivatives

Campbell University

Baylor University

Idaho State University

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

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.

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Is there a number t hat is…

01:10

Is any real number exactly…

This is problem number sixty nine of this tour Calculus, eighth edition, section two point five. Their number. That is exactly one more than its cube. Another way of saying this. If we take the number two b x can one number equal can one number acts equal one more, then that name that number. Cute. So this is what the equation is that we're trying to solve for. And if we rearrange this equation setting equal to zero, we can treat this as finding the route of the function where F is equal to execute, plus one minus X. And we wantto prove that there is a route to this function because then that would prove that there is a solution to the question given. And we're going to use the intermediate value through to confirm that. And with a lot of trial in there, we can choose a certain into role. In this case, we're going to choose an general from negative to to To where at negative, too. The function evaluated at native to gives. Thank you, Terry. Plus three, which is negative. Five and and two. We get eight plus one minus two or seven. So What we see here is that in the interval, from negative to to to the function takes on all the values from negative five to seven. For the reason that the function f is continuous, we see that this function is a polynomial which is always continuous. Ah, for the domain of all real numbers and in the specific interval from negative to to to thing values, much must range between this negative five and the seven. And since eagles from negative too positive, it must take the value zero, which is what we are interested in. We have confirmed in this interval specifically, there exists a number. According to the interment media Valley theme, there exist a number. There exists an X value that makes the statement true that we can figure out index value for which the function F is equal to zero. So we have confirmed that there does indeed exist a number that is exactly one more and it's cute According to the intermediate value, Theo

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