AravindG
  • AravindG
find local maxima and local minima for the function f(x)=sin x-cos x 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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AravindG
  • AravindG
@hartnn
anonymous
  • anonymous
for this you have to find f'(x)
AravindG
  • AravindG
ok ....cos x + sin x then?

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More answers

anonymous
  • anonymous
and then take f'(x)=0
AravindG
  • AravindG
sin x+cos x=0
AravindG
  • AravindG
sinx=-cos x
AravindG
  • AravindG
nw what ?
anonymous
  • anonymous
cos x + sin x = 0 cos x = -sinx
AravindG
  • AravindG
k then ?
AravindG
  • AravindG
why u delete that?
anonymous
  • anonymous
find the value of x
AravindG
  • AravindG
x=-pi/4 isnt it?
anonymous
  • anonymous
no we have to take the value from 0 to 2
AravindG
  • AravindG
then hw ??
anonymous
  • anonymous
take x = 135 degrees
anonymous
  • anonymous
convert it to radians
AravindG
  • AravindG
2.355
AravindG
  • AravindG
x=3pi/4
hartnn
  • hartnn
if x is between 0 to 2pi, then x= 3pi/4 is correct.
AravindG
  • AravindG
k then hw we find local maxima and local minima ?
hartnn
  • hartnn
local only means 'in that interval' , here 0 to 2pi
AravindG
  • AravindG
so what are maxima and minima here ?
hartnn
  • hartnn
so here u'll have only one value , at x=3pi/4 find f(x) when x=3pi/4
AravindG
  • AravindG
also at x=7pi/4 we have only one value so f'(X)= ives 2 values for x isnt it?
AravindG
  • AravindG
f'(X)=0 gives 2 values for x isnt it?
hartnn
  • hartnn
oh yes! i missed that. now its even simpler..... find the second derivate, what u get ?
AravindG
  • AravindG
-sinx +cos x
AravindG
  • AravindG
whats the use of taking second derivative ?
hartnn
  • hartnn
to know which point is max. or min. , u know how ?
AravindG
  • AravindG
nop
AravindG
  • AravindG
is it by substituting 3pi/4 and 7pi/4 in f''(X) and getting the sign to tell which is maxima and minima?
AravindG
  • AravindG
k gt it !!!
hartnn
  • hartnn
yes, if f''(x) > 0 , then max or min ?
hartnn
  • hartnn
ok, good :)
AravindG
  • AravindG
3pi/4 is max other is minima !!
AravindG
  • AravindG
can u check up the answer for the next qn also ?
hartnn
  • hartnn
sure ...
AravindG
  • AravindG
i will post separately

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