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(a) Find the intervals of increase or decrease.(b) Find the local maximum and minimum values.(c) Find the intervals of concavity and the inflection points.(d) Use the inforvation from parts (a)-(c) to sketch the graph. Check your work with a graphing device if you have one.$f(x)=\ln \left(x^{4}+27\right)$

A. Increasing on $x>0,$ decreasing on $x<0$B. $f(0)=\ln \left(0^{2}+27\right)=\ln 27=3.29,$ which is a localminimum. There is no local maximum.C. Concave up on interval $-3<x<3,$ concave down on intervals $x<-3$ and$x>3$D. SEE GRAPH

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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in this question, we can ride out the purity of self ev in the beginning. Suffer product A for the increasing and decreasing the room. First we set if prime because of zero. So you can see we don't have one solution. X equals zero. Um, that means we can see there to serve intervals from connective infinity too. Zero and the from zero to infinity over the first interval. If crime miss less than zero. So the so if the function f is, uh, he crazy over the second her life prince positive. So the function is increasing, and then we can see there is a local minimum at X equals zero with value zero, because to loan off 27. Um, so for policy for Lincoln, charities were set F top of primary cause is zero. Let gives us X equals zero, and the X equals two a pass minus three. So we need to can see their, um we need to consider force of intervals from negative infinity to make the three from three a negative 3 to 0 from 0 to 3 from three. Tweet infinity over the frozen Perot after Prime miss less than zero so the functions can keep down over the second in the 30 interval. If the book from this positive So the front of the functions can keep up over the last interview. If couple promised lesson zeros of the function of contact Tom. And from here we can see there are two inflection points. Um, at X equals two minus three of the X equals 23 And with this information, we can sketch the graph off f. Okay, so there are some inflection point minus three and three, and the one X equals 20 It's a local minimum, which is lonesome are known off 27 and, uh, so busy the functions decreasing and conch if time had a beginning. So it looks like this in the day it's decreasing. And the conch a pup, You crazy income cave up of the increasing contact. Um, she looks like this. We have a new inflection point here in the another inflection point here we have a local minimum at X equals with Europe, So this is

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