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Find $f^{\prime}(x)$.(a) $f(x)=53$ (b) Give a geometric explanation for your result.

(a) 0(b) The TL is the line itself which has slope 0

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 1

Slope of a Curve

Derivatives

Campbell University

Harvey Mudd College

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.

00:57

$$\text { Find } f^{\prime…

03:38

Determine $f^{\prime}(a)$ …

01:47

Find $f^{\prime}(x)$$$…

01:19

Find $f^{\prime \prime}(x)…

02:31

help

02:40

Find $f^{\prime}(x)$ if $f…

0:00

Find $f^{\prime}(a)$.$…

01:21

Solve.If $f(x)=x^{3}-5…

So if f up X is equal 53 what is if what is derivative of this function on what is geometric interpretation of that? So the derivative dysfunction is zero. What does it mean? That is dysfunction is not changing with X has X is changing. This value of dysfunction is not changing. Okay, so if this is X, this is f of X and this is 53 the value of dysfunction. It's not changing with X for all values of X. You have the same when you're 53. Okay, so that is the geometric interpretation function is council.

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