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Short segments of the tangent lines are given at various points along a curve. Use this information to sketch the curve.See Figure 12.

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Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 1

Slope of a Curve

Derivatives

Campbell University

Harvey Mudd College

University of Nottingham

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.

02:33

Short segments of the tang…

01:56

Find the tangents to the g…

06:51

How many tangent lines to …

07:46

01:14

Find an equation for the t…

02:18

Alright, So here we are, given a series of tangent lines at various points along the curve. Given this, we want to sketch the overall curve, which is fairly simply looking at this, we get the general shape of the curve. All we have to do is connect each of these tangent points to give us the curve itself. Doing that, we know we have a tangent line here, so it looks like our slope is gonna be like that. Now we could hear will flatten out a little bit, continuing to flatten out as a tangent lines show. And now we're increasing slope again. And that's a rough sketch of the curve here, given the tangent lines that were that we were initially given.

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