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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.$f(x)=x^{2 / 3}-x$

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 1 / AB

Chapter 4

THE DERIVATIVE IN GRAPHING AND APPLICATIONS

Section 1

Analysis of Functions I: Increase, Decrease, and Concavity

Functions

Limits

Derivatives

Differentiation

Continuous Functions

Applications of the Derivative

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so this function is increasing. Um, from 2.2963 Um And then it's decreasing on the intervals from negative infinity to zero and 00.29632 Positive infinity. The times It's Kong Cave. Ah, con cave up would be never because, as we see here, there is this kink right here. It'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's on Li con cave down from negative infinity to infinity. So there's no conclave up, and there's no inflection point.

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