Calculus

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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 -

    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 -

    Thanks!!! I was getting the first point wrong!

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