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Find the local maximum and minimum values of $f$ using both the First and Second Derivative Tests. Which method do you prefer?$f(x)=1+3 x^{2}-2 x^{3}$

local min: $(0,1) \quad$ local max: $(1,2)$

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 question again, we just write out the first of the narrative and the steak or inability about direct in the beginning. So the first of the 30 because of this in the steak on the curative. Um, because the six minus 12 x eso you? So first, we'll see if we want to find a local maximum low commitment. So first, we just use the front of the director of test in the first quarter to riveter Test. That means we folks on the first of the year it if, if X equals zero, so we have X equals zero. Next request one nine minutes way have three intervals from negative infinity to zero from 0 to 1 and the from one to infinity. So for the first interval, the first of the directive, um, it's inactive. So stick racing on the funkiest be crazy in the only second to roll the first of the purity of its positive. So it's increasing. And for the last interval, the first of the purity reason active again. So it's decreasing. So for this result, we can see that at X equals zero, it's requesting first, the increasing That means it's a local. Many men at X equals zero with the value f zero because the one and the attacks equals one bullets left. The functions increase you only cerise. The function is decreasing. So we have a local next at X seacoast, one with value if one equals 22 So this is the first or the purity of test for local maximum low commitment. And we can also do the second a direct your test. I'm from here. We already find the critical points, which is X equals zero, Mexico's toe one. And we have this second narrative and becoming so for exit close to zero. The second of curative at zero equals 26 which is positive. That means it's a long cold, meaning one, the same as I will result before and the four X equals to one. The second narrative at one equals to mind sixties inactive. So it's a no cold maximum by the second degenerative test and we can choose one off this may 3rd. Yes, we want because, like they give Fastness

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