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(a) Find the intervals on which $f$ is increasing or decreasing.(b) Find the local maximum and minimum values of $f .$(c) Find the intervals of concavity and the inflection points.$f(x)=x^{2}-x-\ln x$

A. $f(x)$ is increasing when $x \in(1, \infty)$$f(x)$ is decreasing when $x \in(0,1)$B. There is local minimum at $x=1$There is NO local maximumC. The graph is concave up on $(0, \infty)$

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 3

Derivatives and the Shapes of Graphs

Derivatives

Differentiation

Applications of the Derivative

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Idaho State University

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.

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) Find the intervals on …

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in this program, its first find out the first of the narrative and the second the narrative of that. So for pate, we're asking are asked to find the increasing and decreasing her bro. We need to set this, um, first of the curative because with Europe. So by this factory ization, we have toasted oceans X equals two, uh minus 1/2. And it's Sequels to what funds? We don't need to use this solution because that will mean off is from zero to infinity. So this X equals minus one Have is also a little men off ever. So we don't need to use this solution. Now we use the second solution. X equals to one to separate the domain to to serve intervals from 0 to 1 and the from one to infinity. So only 0 to 1 on this interval. The frost in iterative Yes, negative. That means the pharmacy is the cuisine on the second terrible in the first degree. Relative is positive. The function is increasing. That means we have a loco many men that ex seacoast, one with value, care for one. You close to the area now for the second part, we want to find out the concave. It is, but are a steak on the purity because two to pass one over X Square, which is strictly positive. All the domain that means the function function. Eighth Yes, Kong Caves. How poured on the own Stoneman, so there's no inflection point.

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