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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