what is the maximum value of the function f(x)=e^x/3sin(2x) on the interval (0,3.142)?

Answer 1

Its so much easier to get other people to do your homework for you isnt it...........just a hunch!

Answer 2

2

Answer 3

2

Answer 4

f(x) = (e^x)/(3sin2x)
u = e^x (top)
v = 3sin2x (bottom)
du/dx = 6cos2x (differentiate the top to use later)

f'(x) (differential) = (du/dx * v - dv/dx * u)/(v^2) (quotient rule)

= ((e^x)(3sin2x) - (e^x)(6cos2x))/(9sin^2(2x))
which = 0 (since max. value is a turning point where gradient is 0)

Since x is positive
(e^x)(3sin2x) - (e^x)(6cos2x) = 0
(e^x)(3sin2x - 6cos2x) = 0
3sin2x - 6cos2x = 0 (since e^x can't equal 0)
sin2x = 2cos2x
tan 2x = 2
x = (tan^-1(2))/2 ~= 0.553574
f(0.553574) ~= 0.648258

Which isn't the answer, because Excel shows it's a minimum (prove this mathematically by differentiating the differential of f(x) and showing that it is positive). Excel also shows that the maximum value is infinity. If you don't count this then the answer is ~ -3.118432. Work this out by finding the next value of tan^-1(2), which is ~ 4.248741, and dividing this by 2, then running that through the function to find f(x).

Answer 5

If your f is equal to the ratio of 6.566 and this with e^ being of the same value as the equation of f- the total of the sum then the correct response would be the answer you are seeking from the correct responder.

Answer 6

The equation could probably do with a few more brackets to make it clear. At present there are a few options as to what it is.

Answer 7

You know what Rach? I have absolutely no idea. Sorry dear I never did get to grips with that complex maths stuff. Why don't you just use numbers?

Answer 8

the meaning of life ....42

Answer 9

3.142