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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.$f(x)=x^{3}-12 x+2$

A. increasing: $(-\infty,-2),(2, \infty) \quad$ decreasing: $(-2,2)$B. local max: $f(-2)=18 \quad$ local min: $f(2)=-14$C. concave down: $(-\infty, 0) \quad$ concave up: $(0, \infty) \quad$ infl. point: $f(0)=2$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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for this problem its first right out euro tips the front both love for so that he right here on the second narrative off f So pat A We set if prime Michels to zero So we have X equals to pass minus two. That means we need to consider the recipient. How goes negative infinity to connective to connective 2 to 2 and the two to infinity First on the first interval. If prime is positive safety increasing on the second of life promise negative So it's decreasing I'm allows him however, if crimes positive again city increasing and from part of a we know that when X equals two minus two So there's a local, uh, maximum with value f to you crossed very king and at X equals to two is a local minimum with the value of two equals two minus 14 and the pop See, we said that if double Primakov zero we only have one solution X equals zero So we have to sub intervals from negative infinity to zero and the from zero to infinity on the first sub in trouble If the prime is negative so to come cave down world and Ah, on the second row. If that about Prime miss positive. So it's conch it upward. So we have the inflection point at X equals zero, and we are ready to graft such function on the coordinates. So first we can label out some, um, create a point and the inflection points. So, uh, XY caused a minor stories. A local maximum exit question, too, is a local Milliman. And the inflection point is, every issue should be X equals 20 Um, someone X equals zero. The functioning crystal too. Yeah. Label the inflection point here. Okay, on Now we already the graph. So from negative infinity connective to the function is increasing the U eventually and it's concave down. So it looks like this. And then when he passed through this local maximum, it's d crazy and also calm cave down. Now we passed this inflection point You changes that can cavity to become cave up And we passed this commitment you see increasing again. So on the graph Looks like it's This is an X Texas Why exists the three Why existed that this is a

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