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Sketch the graph of a function that satisfies all of the given conditions.Vertical asymptote $x=0, \quad f^{\prime}(x)>0$ if $x<-2,$$f^{\prime}(x)<0$ if $x>-2(x \neq 0),$$f^{\prime \prime}(x)<0$ if $x<0, \quad f^{\prime \prime}(x)>0$ if $x>0$

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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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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.

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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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Sketch the graph of a func…

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Sketch a graph of a functi…

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Sketching graphs Sketch a …

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one example for the functions satisfy on those condition. Eyes looks like this. So we first we lay both some point, which is minus two in zero. Um, so one example looks like lips. Um, so increasing first, then when on the function past this minus two, it turns out to be decreased, decreasing. And because he has a horizontal sympathetic here. So we have some likeness. And when x is greater than zero, you also has the horizontal synthetic, and, uh, it's depressing. And there, concurrently, looks like this so we can gruesome anesthetize here. So for on the interval from minus infinity to to it's, um increasing and, uh, con cave no. And on the interval from minus 2 to 0 is decreasing in the conclave up. Sorry. It's also come gift. Um, And on this side, it's decreasing in the conclave down. So this is Khan K pop in effect, and that's it. This is one of league's impossible. We can generate a lot of different examples, but this is one

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