+128408 y = 4sin^2(x) - 12sin (x) + 7
Take the derivative and set to 0
y '= 8sinxcosx - 12cosx = 0
So
8sinx cos x - 12cos x = 0 factor
4cos (x) ( 2sin (x) - 3) = 0 set each factor to 0 and solve for x and we have that
x = pi/2 or 3pi/2 sin x = 3/2 ( this is not possible )
So....the max occurs at x = 0
At pi/2 the function value is
4sin^2(pi/2) - 12 sin(pi/2) + 7 = -1
At (3pi/2) the function value is
4sin^2 (3pi/2) - 12 sin (3pi/2) + 7 =
4 + 12 + 7 =
23 = the max value
