Question

Find the maximum and the minimum values of th function.
y=2sin(x)+sin^2(x)

Answer 1

First find y' i.e., differentiate the
let y=2sin(x)+sin^2(x)
then
y'=2cos(x)+2sin(x)cos(x)
then for maximum or minimum y'=0
i.e., is
2cos(x)+2sin(x)cos(x)=0
then find the values.....

Answer 2

then subtitute this values in y'' then you will get max and min...

Answer 3

no need to find f" , stop at f' that's enough to consider max/min.
don't forget + 2kpi (since it 's a period function)

Answer 4

No you have to substitute f'(i.e., y') values in f'' (i.e., y'')

Answer 5

why? f" is used to find out concavity , inflection points and consider the relative max/min. However, for the part relative max/min, this f" just to know there is some max/min or not, it doesn't show the value of max/min

Answer 6

Hint :
y=2sin(x)+sin^2(x)
it would be minimum when sin(x) = -1 and
it would be maximum when sin(x) = 1