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Refer to Figures $8,9,$ and $10 .$ In each case, choose another point on the tangent line to determine the slope of the curve at $P$.

$$-4 / 3$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 1

Slope of a Curve

Derivatives

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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.

01:50

Refer to Figures $8,9,$ an…

01:24

03:48

Copy the following figures…

03:12

The point P(9, 1) lies on …

09:19

In Problems 90-96, use Des…

03:04

In exercises 9 and $10,$ f…

01:30

Refer to Figure $93 .$ How…

01:52

Find the equation of the t…

02:03

04:12

Alright, here we have a graph given to us where we are asked to find the slope of the curve at point P. We'll be using some basic calculus to determine this is all as well as our basic slope formula, where M is equal to y tu minus y one Oliver x two minus X one Now to determine the slope at point 87 On this curve, we've drawn a tangent line through it. We can easily find the slope of the tangent line if we just find another point along it. We've already been given 0.0.87 We need to find one more. Let's use this one right here. That gives us point c 11 three with that and the other the other point that we have. We can now plug this into our slope formula she gives us M is equal to three minus seven all over 11, minus eight. Simplifying this. We get negative four all over three and that gives us our slope so we can conclude that our slope at point 87 is equal to negative for over three

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