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find local maxima and local minima for the function f(x)=sin xcos x
0<x<2
 one year ago
 one year ago
find local maxima and local minima for the function f(x)=sin xcos x 0<x<2
 one year ago
 one year ago

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uzumakhiBest ResponseYou've already chosen the best response.0
for this you have to find f'(x)
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
ok ....cos x + sin x then?
 one year ago

uzumakhiBest ResponseYou've already chosen the best response.0
and then take f'(x)=0
 one year ago

uzumakhiBest ResponseYou've already chosen the best response.0
cos x + sin x = 0 cos x = sinx
 one year ago

uzumakhiBest ResponseYou've already chosen the best response.0
no we have to take the value from 0 to 2
 one year ago

uzumakhiBest ResponseYou've already chosen the best response.0
convert it to radians
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
if x is between 0 to 2pi, then x= 3pi/4 is correct.
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
k then hw we find local maxima and local minima ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
local only means 'in that interval' , here 0 to 2pi
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
so what are maxima and minima here ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
so here u'll have only one value , at x=3pi/4 find f(x) when x=3pi/4
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
also at x=7pi/4 we have only one value so f'(X)= ives 2 values for x isnt it?
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
f'(X)=0 gives 2 values for x isnt it?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
oh yes! i missed that. now its even simpler..... find the second derivate, what u get ?
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
whats the use of taking second derivative ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
to know which point is max. or min. , u know how ?
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
is it by substituting 3pi/4 and 7pi/4 in f''(X) and getting the sign to tell which is maxima and minima?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
yes, if f''(x) > 0 , then max or min ?
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
3pi/4 is max other is minima !!
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
can u check up the answer for the next qn also ?
 one year ago

AravindGBest ResponseYou've already chosen the best response.0
i will post separately
 one year ago
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