Yahoo Answers: Answers and Comments for MIN & MAX? (Pls show all the sequences for better understanding) ☺? [Mathematics]
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From Anonymous
enGB
Sat, 11 Nov 2017 08:25:48 +0000
3
Yahoo Answers: Answers and Comments for MIN & MAX? (Pls show all the sequences for better understanding) ☺? [Mathematics]
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https://uk.answers.yahoo.com/question/index?qid=20171111082548AA0h24J
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From Snugglebunnie101: OK, here you go sweetheart :)
i) y = cosx ...
https://uk.answers.yahoo.com/question/index?qid=20171111082548AA0h24J
https://uk.answers.yahoo.com/question/index?qid=20171111082548AA0h24J
Sat, 11 Nov 2017 09:30:41 +0000
OK, here you go sweetheart :)
i) y = cosx  sinx
dy/dx =  sinx  cosx
dy/dx = 0
 sinx  cosx = 0
 sinx = cosx
 sinx/cosx = cosx/cosx
 tanx = 1
x =  π/4
Another solution is :
x = ( π/4) + π = 3π/4
Now just substitute these values into the original equation :
y = cos ( π/4)  sin ( π/4) = cos (π/4) + sin (π/4) = (1/√2) + (1/√2) = (2√2)/2 = √2
y = cos (3π/4)  sin (3π/4) = ( 1/√2)  (1/√2) = ( 2√2)/2 =  √2
Maximum value = √2
Minimum value =  √2
ii) y = 3sinx + 4cosx
dy/dx = 3cosx  4sinx
dy/dx = 0
3cosx = 4sinx
3cosx/cosx = 4sinx/cosx
3 = 4tanx
tanx = 3/4
tan²x = 9/16
tan²x + 1 = 9/16 + 1
sec²x = 25/16
cos²x = 16/25
cosx = ±4/5
sinx = ±√(1  cos²x)
sinx = ±√(1  16/25)
sinx = ±√(9/25)
sinx = ±3/5
Now again, just substitute these values into the original function :
y = 3(3/5) + 4(4/5) = 9/5 + 16/5 = 25/5 = 5
y = 3 ( 3/5) + 4 ( 4/5) =  9/5  16/5 =  25/5 =  5
Maximum value = 5
Minimum value =  5
iii) y = 2x  tanx
dy/dx = 2  sec²x
dy/dx =0
2  sec²x = 0
2 = sec²x
2 = 1/cos²x
2cos²x = 1
cos²x = 1/2
cosx = ±1/√2
x = ± π/4
So x = π/4 since due to the restriction 0 < x < π
Another solution is :
x =  π/4 + π = 3π/4
Now finally, substitute these values of 'x' into the original equation to yield the following :
y = 2(π/4)  tan (π/4) = (π/2)  1
y = 2(3π/4)  tan (3π/4) = 3π/2  ( 1) = (3π/2) + 1
Maximum value : (π/2)  1
Minimum value : (3π/2) + 1
Hope this helps !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
P.S. (Don't forget to vote me best answer as being the first to correctly answer your question!)

From ?: .0
https://uk.answers.yahoo.com/question/index?qid=20171111082548AA0h24J
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Sat, 11 Nov 2017 08:27:14 +0000
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