For each of the given functions, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the coordinates of all local extrema. f(x)= 2x^2 - 16ln x

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

For each of the given functions, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the coordinates of all local extrema. f(x)= 2x^2 - 16ln x

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

according to the function, x∈(0,+∞), its derivative should be f'(x)=4x-16/x. let f'(x)=4x-16/x=0, x=2. the change of x, f'(x), and f(x) is as following: x (0,2) 2 (2,+∞) f'(x) - 0 + f(x) decrease 8-16ln 2 increase from above, we can see that the interval on which f(x) is increasing is (2,+∞), and the interval on which f(x) is decreasing is (0,2).
what is the local minimum
the local mininum, naturally, is f(2)=8-16ln 2

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

i got the point (2,-2.5) but she circled the -2.5 and i dont understand that
it's not -2.5, 8-16ln2≈-3.090 , not -2.5
duh...lol
could you help me on one more like this?
\[f(x)= 4x ^{3} + 3x ^{2} +2\]
i'd love to. well, first we should remember the basic derivatives!? for example, f(x)=x^a, then f'(x)=ax^(a-1). f(x)=c (c is a constant), then f'(x)=0. also the algorithm of derivatives, such as [f(x)±g(x)]'=f'(x)±g'(x). so f(x)=4x^3+3x^2+2, f'(x)=12x^2+6x
okay i understand that
great. so just now did you want me to work out the intervals that are increasing or decreasing?
yes and the local extrema please
okay. first, it may be a good habit to do a factoring with the derivative (at least my teacher told me like this) because it will be convenient to calculate. f'(x)=12x^2+6x=x(12x+6). next, we are sure that the derivative at local extrema should be 0. let f'(x)=x(12x+6)=0. so you can work out the solutions of x here very fast, x1=0, x2=-1/2.
notice here that the domain of definition of the function is R. split it into intervals and points according to the solutions of x, as (-∞,-1/2), -1/2, (-1/2,0), 0 , (0,+∞)
okay so far?
hold on working on it
so it is decreasing at 0,0 and increasing at 0,0
the change of x, f'(x), and f(x) is as following: x (-∞,-1/2) -1/2 (-1/2,0) 0 (0,+∞) f'(x) + 0 - 0 + f(x) ↗ 9/4 ↘ 2 ↗
the +/- of the f'(x) stands for whether f'(x) is positive or negative. when f'(x)>0, increases; when f'(x)<0, decreases. so it is directly perceived that the increasing intervals are (-∞,-1/2) , (0,+∞); the decreasing interval is (-1/2,0). the maximum value is f(-1/2)=9/4 and the minimum value is f(0)=2
oh! now i get you
(^ ^) love to communicate with you.
what do you mean?
what?
love to communicate with you?

Not the answer you are looking for?

Search for more explanations.

Ask your own question