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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.$g(x)=200+8 x^{3}+x^{4}$

A. $f(x)$ is increasing when $x>-6$ and decreasing when $x<-6$B. Local minima occurs at $x=-6$ and the local minimum value is $-232$C. CU on $(-\infty,-4),(0, \infty)$inflection points: $(-4,-56),(0,200)$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, um for us right out to the narratives off a g. So for part a one, we just said that your prime cost is your own. So we have X equals zero and the extra cost of minus six. Those are the critical point. And then we have took with your point. That means we need to consider three sub intervals, several negative infinity to minus stsnegative six protective 6 to 0 and often zero to infinity. On each interval, We only care about a sign of your prime. So in the first interval that you promise less than zero on the next two interval that you promise are great and zero on them Use own minus infinity to minus six. The function is decreasing and the the phone she is increasing over the last two in the rose. This result also cue salsa Loco Milliman which yes, at XY question mind six with value. Ah, the G minus six. Because tu minus 232 Ah, So the next part of we are going to find the other communities. So we set the second of the relatively close to zero. So we have two solutions. X equals zero Next. Tequesta minus four lemons. We need to consider to raise up intervals from negative infinity. Tomek, therefore, throw negative 4 to 0 on the front zero to infinity. Only drop them. We only care about a sign off. G have a prime Such a double prime miss positive over the frozen hero to topple Prime Miss Negative over the second Terrible and the Jew Top of promise Positive again on the last in Congo. So we know on the first in, however, the functions can keep up. This on the second over of the functions concrete down on the last in trouble and functions country pop again. That means that we have to your collection points which is at X equals two minus for in the X equals 20 because the community is that different. Okay, so can buy off this information. We can sketch a graph off keep so let's forced labeled some quicker points minus six and zero. And the way we also need to lay partly inflection coins. Okay, so the funkiest decreasing. First we when x equals two mind six has a local Milliman Daisy increasing started his immense for so is increasing. But, um, once X equals two minus for like an cavities, a different. She looks like something like this. And then it's another inflection point. IQ attacks equals zero. So you have something like this. And so basically we have to inflection points, and we have one critical points, thanks.

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