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Problem 25

a. Find the open intervals on which the function …

01:24
Problem 24

a. Find the open intervals on which the function is increasing and decreasing.
b. Identify the function's local and absolute extreme values, if any, saying where they occur.
$$
f(\theta)=6 \theta-\theta^{3}
$$

Answer

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Video Transcript

all rights of empathy. No. Is six data my understanding? But today the derivative that primary data is just six minus three. Get it squared. So if you want to find the critical points, where is F prime nickel to zero. What we need They squared to be two, or in other words, data is plus or minus three two. So let's find the intervals where f is increasing and decreasing. So we'LL look at the derivative at around our critical points soon crime If he and it is they did squared is greater than two then have power is going to be negative So negative, negative and positive Okay, And then So that shows us that, uh, it's decrease saying and then increasing, decreasing It's a decreasing from mice Infinity Demise for two Do you hear anything from I want to tell me And an increasing between minus route Too hungry too. And then we see we have a local men had negative too. Then we can get in and we kids minus for two for the value And then we have a local max at Reed Tio uh, changes from increasing decreasing, but the value of for it too. And there's no absolute max tracks absolute men, because this is a cubic it's going to be decreasing and then go on decrees down, so it's gonna be no value that's larger or smaller than any other.