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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.$f(x)=5+12 x-x^{3}$

A. $f$ is increasing when $f^{\prime}$ is positiveB. $f$ is decreasing when $f^{\prime}$ is negativeC. $f$ is concave up when $f^{\prime \prime}$ is positiveD. $f$ is concave down when $f^{\prime \prime}$ is negativeE. Inflection occurs at $x=0$

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 here the interval of increase, I would be from negative to to to the intervals of decrease would be from negative infinity to negative two. And from two to positive Infinity. Uh, the conch A up interval would be from negative infinity to to and the Khan cave down. Um, the conclave up interval would be from negative infinity, uh, to to. And then what we see here is actually where it starts to to change the Baby Kong cave conclave up from negative infinity to zero. And it's calm. Cave down from zero to positive infinity, which means that zero would be an inflection point.

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