Posted by deepak on Tuesday, May 24, 2011 at 5:01am.
find the maximum value of √3 cosθsinθ.???

mathematics  drwls, Tuesday, May 24, 2011 at 5:37am
You get a maximum when the derivative is zero.
ã3 sin ƒÆ cos ƒÆ = 0
tan ƒÆ = 1/ã3
ƒÆ = 30 degrees
ã3 cosƒÆsinƒÆ = 3/2 + 1/2 = 2
check: If theta = 29 degrees,
ã3 cosƒÆsinƒÆ = 1.5149 + 0.4848 = 1.9997
If theta = 31 degrees,
ã3 cosƒÆsinƒÆ = 1.4847 + 0.5150 = 1.9997
So it looks like the maximum is 2.
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