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Find the fourth root of 7 to six decimal places. Hint: find a zero of $x^{4}-7$ Why does this produce the root?

1.626577

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 11

Newton s Method

Derivatives

Missouri State University

Campbell University

Oregon State 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.

01:22

Find all the real-number r…

00:15

00:33

02:06

Solve. Use a calculator to…

01:03

Use the fact that $\sqrt{7…

03:08

More root finding Find all…

Okay, so we want to solve the falling for exits, would start taking the Natural law Global sites. Since we know that these two bases are part numbers on, they're not the same. So we need to bring down that power of X. Okay, so this is equal to one or the natural log of two plus three x natural log of two. And now I'm gonna move this three x natural log to to our left hand side so we can isolate that term. And in fact, out of X. So what do we get? We get negative three x match. A lot of to minus four X Macha Log of seven. That's equal to the natural log on to Okay. And now I'm gonna fact throughout this X that we have in common and then divide by this term here. So we get X is equal to the natural. Log on to all over Negative three. Natural log to minus four at your log of seven. Now, let's also put this into our calculator to see what we yet Okay, So this is approximately a negative zero point several 70

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