Posted by Anonymous on Friday, June 22, 2012 at 8:13am.
Find all points on the graph of the function f(x) = 2 sin(x) + (sin(x))^2 at which the tangent line is horizontal. Consider the domain x = [0,2π).

Calculus  Reiny, Friday, June 22, 2012 at 8:34am
f'(x) = 2cosx + 2sinx(cosx)
= 0 when the tangent is horizontal
2cosx(1 + sinx) = 0
cosx = 0 or sinx = 1
if cosx = 0
x = π/2 or 3π/2
f(π/2) = 2(1) + 1 = 3
f(3π/2) = 2(1) + 1 = 1
so we have two points, (π/2 , 3) and (3π/2 , 1)
if sinx = 1
x = 3π/2 giving us the same point as above
there are two points (π/2 , 3) and (3π/2 , 1)

Calculus  Anonymous, Friday, June 22, 2012 at 10:11pm
Thanks!!! I was getting the first point wrong!
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