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Determine the derivative at the given point on the curve using equation (2).$f(x)$ as defined in Exercise 6.

$1 / 4$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 1

Slope of a Curve

Derivatives

Campbell University

Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

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.

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the function is fx equals the absolute value of X, Which is -1. If X is negative and active access palliative. Now they use the definition of derivative to find the derivative of this function. Since the expression of this function is different when X is positive or negative. We should discuss it in two different situations. Yes. Tax is negative. Yeah. Have prime mats echoes Limit Age goes to zero. F X plus eight is just miners. X plus eight, miners, miners max over eight which equals minor sage over age, which is negative. What? And do you have access positive? Yeah. Primary echolls. That limit Acts goes to zero. Yes passage. My nurse acts over eggs, Which is a judge or a jury. Articles one enhance. Well, Alex is negative. Its derivatives in my nurse one And the exit positive. It's derivative is one. But what if X echo zero? So it's derivative from the left echoes -1, which is not one. The narrative from the right. This is to see this function is yes. Don't have a derivative at the zero. And hence this function is not different insurable at the point is terrible.

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