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(a) Use a CAS lo differentiate the function $ f(x) = \sqrt \frac {x^4 - x +1}{x^4 + x +1} $and to simplify the result.(b) Where does the graph of $ f $ have horizontal tangents?(c) Graph $ f $ and $ f' $ on the same screen. Are the graphs consistent with your answer to part (b)?

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a. $\frac{3 x^{4}-1}{\sqrt{\frac{x^{4}-x+1}{x^{4}+x+1}}\left(x^{4}+x+1\right)^{2}}$b. $x=\pm \sqrt[4]{\frac{1}{3}}$c. $x=\pm 1 / \sqrt[4]{3}$

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Campbell University

Oregon State University

Harvey Mudd 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.

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.

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(a) Use a CAS to different…

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a) Graph the function f(x)…

is this Probably require a calculator I'LL skip the detail our if you want to do with yourself which is quite lengthy, you you have to use So the general which the numerous are the denominator up it is and you have to beauty pride by that the river TV inside which there you have to compute it by using the kosher This is quite a lengthy So I'll give you i'll leave the details to you and the questions allow you to use a calculator for horizontal attention You simply solved the equation The relative equals zero and go from there.

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