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Find $ f'(x) $. Compare the graphs of $ f $ and $ f' $ and use them to explain why your answer is reasonable.$ f(x) = x^4 - 2x^3 + x^2 $

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$$f^{\prime}(x)=4 x^{3}-6 x^{2}+2 x$$

00:21

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Missouri State University

University of Michigan - Ann Arbor

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.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

01:56

Find $ f'(x) $. Compa…

01:30

02:28

Find $f^{\prime}(x) .$ Com…

02:13

Find $f^{\prime}(x)$. Comp…

01:39

01:44

01:25

Find $ f'(x). $ Check…

04:55

(a) If $ f(x) = x^4 + 2x $…

he has cleared. So when you right here. So we have our original, and we're gonna find our derivatives, which is equal to X the fourth minus two ex cute bliss X square. Take the derivative. When we get for X Cube minus six X square close to acts, we're gonna graph it our original I'm gonna do in black and are derivative Odd zoo in red. So we have thio Note that are derivative is positive when the originals increasing and negative When the original is decreasing And whenever FF X is at a local minimum or max the derivative is equal to zero.

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