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(a) Find the intervals on which $f$ is increasing or decreasing.(b) Find the local maximum and minimum values of $f .$(c) Find the intervals of concavity and the inflection points.$f(x)=2 x^{3}+3 x^{2}-36 x$

A. $+(-\infty,-3),-(-3,2),+(2, \infty)$B. The local maximum is $f(-3)=81$The local minimum is $f(2)=-44$C. Inflection point at $x=-\frac{1}{2}$Concave downward in $\left(-\infty,-\frac{1}{2}\right)$Concave upward in $\left(-\frac{1}{2}, \infty\right)$

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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for this program we're going toe if I thean creasing and equipped, interval the local medicine man, local minimum and the concave deities. So let's just take the purity of twice so the first of the purity. Because to our six x square plastics, X minds the basics so in effect this into six times X plus three times X minus two and there for the sake of the dirt, it's just two of X plus six. So off this reader follows follows the power room by taking a curative so pate for the increasing decreasing interfere with you too. Ah said this first of the narrative because zero So we have two solutions which is X equals 22 and X equals two minus three. So this to solutions sleet separates that domain two or three parts the first part of a B minus infinity to minus three the second parties from minus 3 to 2 the last parties from two to post here For you Kennedy so on the first inter role as prime affects is uniformly positive. That means this is increasing on the sick interval the say the frozen maturity. If it's negative, them use over this interval. Speak, raising and for the last time, Perot, the first of the irritating is part of people again. So it's increasing. And from here we can find thoughts. We have a local make Semen at X equals two minus three because it's increasing for us. That d crazy. Today's a peak, so the value will be 81 in the way. We also has half a local minima at X equals tube because it's decreasing first, the increasing so it's f off to the Valley will be minus 44. As for Lacan charity apart. See, it's related to the second of the table we sent to the second of narrative because zero. So we have 12 express 60 cause zero. So we have X equals minus 1/2. No, we have tools up intervals from negative infinity to a negative on have and the front negative one have to positive community. So, over the first informal a steak on the directive, it's negative. The music's conclave downward over the second. Terrible. The second videotape is positive. So it's the controversies operate, and we indeed have a reflection point at X equals. The one hat minus would have because, um, on the two sides off this minus 1/2 like activities that different

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