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In each part state the $x$ -coordinates of the inflection points of $f .$ Give reasons for your answers.(a) The curve is the graph of $f$ .(b) The curve is the graph of $f$ '(c) The curve is the graph of $f^{\prime \prime}$

A. No inflection pointsB. $x=2,4,6$C. Inflection occurs at $x=1,7$Hint $: f^{\prime \prime}(x)$ must change sign

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 3

Derivatives and the Shapes of Graphs

Derivatives

Differentiation

Applications of the Derivative

Campbell University

Oregon State University

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.

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In each part state the $ x…

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In each part state the X-c…

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7. In each part state the …

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The graph of $f^{\prime}$ …

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(a) Graph $f(x)=\sqrt[3]{x…

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The graph of the second de…

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Inflection Point Consider …

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$\begin{array}{l}{\text { …

Okay, So, um, for Poppy. If the given graph is forever so clearly, we have to infraction punk X equal at X equal to three. And the X equals 25 because, um on both side off this given point, the continuities are different. And for part B, if the given graph is for F prime, the inflection point will be X equals two two X equals 24 and XY close to six. Because this is the point when, uh so, for example, when X equals 22 Oh, it's left. The frost of the narrative is increasing. Annoys writer first of the narrative istea crazy. That means the second narratives size I was changing at this single point. And for this for the same reason when X equals two foreign the X equals of seven. Those are the inflection points. And for part C if the given graph is full um, the second narrative. So we only have to quit inflection point when x seacoast won the X equals 27 not when X equals before. This is not an inflection point, because on its both size, um, on both side, um, the sign off the second narrative remains positive, So X equals before is not an inflection point, but X equals Tawan Nick X equal to seven i infraction points.

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