find-a-the-intervals-on-which-f-is-increasing-b-the-intervals-on-which-f-is-decreasing-c-the-open-12

Question

Find: (a) the intervals on which f is increasing, (b) the intervals on which f is decreasing, (c) the open intervals on which f is concave up, (d) the open intervals on which f is concave down, and (e) the x-coordinates of all inflection points.
$f(x)=x^{2 / 3}-x$

Carson Merrill · Accepted Answer

so this function is increasing. Um, from 2.2963 Um And then it&#x27;s decreasing on the intervals from negative infinity to zero and 00.29632 Positive infinity. The times It&#x27;s Kong Cave. Ah, con cave up would be never because, as we see here, there is this kink right here. It&#x27;s not differential at this point. Um, but everywhere, uh, the derivative function, as we see is, has a negative slopes. That means that it&#x27;s on Li con cave down from negative infinity to infinity. So there&#x27;s no conclave up, and there&#x27;s no inflection point.

Carson Merrill · Answer

So here there&#x27;s no interval decrease. It&#x27;s all an interval of increased from negative infinity to positive infinity. Uh, the graph is Kong Cave. Uh, graphics con cave up at this point right here. So from negative 0.52 infinity, the graph would be considered con cave up. Um, And then the graph is con cave down from negative infinity to negative 0.5. And that tells us that X equals negative. 0.5 is an inflection point.

Carson Merrill · Answer

So if we look at this graph, we see that it&#x27;s increasing from negative 1 to 0 and then from positive one to infinity. And it&#x27;s decreasing from negative infinity to negative one and then zero toe one in terms of being, uh, connectivity, it&#x27;s Kong cave up from conclave up from negative infinity. If we look at this graph here we see it xcom cave, uh, from negative infinity to positive infamy. And as clear here is, just there&#x27;s this. It&#x27;s not differential at this point right here causes the sharp turn. Um, so I tells us that there is no inflection point and there&#x27;s no areas where it&#x27;s conch eight down.

Carson Merrill · Answer

so looking at a graph here, we can look at the, um, derivative crafted, get a better view of things. So we see that, um, here that the graph is increasing from 0.25 to infinity and and it&#x27;s decreasing from negative. Infinity 2.25 Then we see that, uh, it&#x27;s Kong cave up. The graph is Kong. Keep up. So here it becomes the graph goes the negative. We&#x27;re assuming here and we see that the graph is conch it up. Um, all the way from here. So from 02 infinity, the graph is Khan gave up and from negative infinity to zero. Ah. So the graph is Khan gave up from negative infinity to negative 0.5 and then from negative 0.52 zero, it&#x27;s concave down and then from zero to infinity, its conclave up. So the inflection point to be a negative 0.0.5 and zero

Carson Merrill · Answer

this graph here as we see as increasing from negative infinity Positive Indy. So there is no interval of decrease. We also see that, um, there is Khan cavity at Kong Cave, up from zero to Infinity Kong cave down from negative infinity to zero, so zero would be the only inflection point.

Carson Merrill · Answer

So here&#x27;s our graph. Always see that the, um increases from zero Teoh pi over two. And the decrease is from negative pi over 2 to 0. Then, in terms of con cavity, we see that, um, it is Kong Cave Conch eight up from hi over to from from negative one Teoh negative 0.439 It&#x27;s con cave up. And then from negative 0.439 20 it&#x27;s con cave down then from actually from negative 0.439 all the way to positive 0.439 It&#x27;s Khan came down, Uh, And then it goes Con Cape, up from 0.4392 positive one that tells us that 10.439 and negative 0.439 are the inflection points of this graph.

Problem

Find: (a) the intervals on which f is increasing,…

Problem 26 Easy Difficulty

Find: (a) the intervals on which f is increasing, (b) the intervals on which f is decreasing, (c) the open intervals on which f is concave up, (d) the open intervals on which f is concave down, and (e) the x-coordinates of all inflection points.
$f(x)=x^{2 / 3}-x$

Answer

a. $x \in\left[\frac{8}{27},+\infty\right)$
b. For $f(x)$ decreasing $x \in\left(-\infty, \frac{8}{27}\right]$
c. $x \in(-\infty, 0),(0, \infty)$
d. There is no point of inflection.

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Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals

Anna Marie V.

Heather Z.

Samuel H.

Michael J.

Precalculus Review - Intro

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a. $x \in\left[\frac{8}{27},+\infty\right)$b. For $f(x)$ decreasing $x \in\left(-\infty, \frac{8}{27}\right]$c. $x \in(-\infty, 0),(0, \infty)$d. There is no point of inflection.

Calculus Early Transcendentals

Anna Marie V.

Heather Z.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

Howard Anton, Irl Bivens, Stephen DavisCalculus Early Transcendentals

Anna Marie V.

Heather Z.

Samuel H.

Michael J.

a. $x \in\left[\frac{8}{27},+\infty\right)$
b. For $f(x)$ decreasing $x \in\left(-\infty, \frac{8}{27}\right]$
c. $x \in(-\infty, 0),(0, \infty)$
d. There is no point of inflection.

Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals