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Let $f(x)=x^{3}-2 x-7,$ (a) show that a root of this function lies in the interval $(1,3),$ (b) Determine the equation of the tangent line to this curve at $x=2,$ and determine its $x$ -intercept. (c) Determine the equation of the tangent line to the curve at the $x$ -intercept found in (b) and determine the $x$ -intercept of this tangent line. (d) Determine the equation of the tangent line to the curve at the $x$ -intercept found in (c) and its $x$ -intercept. (e) Continue the above and produce a root of the given function to six decimal places.

(a) $f(1)<0, f(3)>0$ so a root is in (1,3)(b) $y=10 x-23,2.3$(c) $y=13.87 x-31.334,2.2511896$(d) $y=13.203564 x-29.8174032,2.443357$(e) 2.258259

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 11

Newton s Method

Derivatives

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

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.

02:19

Find $f^{\prime}(x)$ and f…

01:40

a. Find the derivative of …

03:36

02:52

Find an equation of the ta…

03:54

a. For the following funct…

01:12

01:57

Find the particular equati…

01:50

a. Find the slope of the t…

06:25

Find(A) $f^{\prime}(x)…

02:55

(a) find an equation of th…

00:53

Finding an Equation of a T…

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