Find the critical numbers, the extrema, and the interval of increase and decrease for f(θ)=2cos(θ)cos²(θ).
a) Critical numbers: π/2, π; Extrema: Maxima at π/2, Minima at π; Increasing on (−[infinity],π/2), Decreasing on (π/2,π)
b) Critical numbers: π; Extrema: Maxima at π/2, Minima at π; Increasing on (−[infinity],0), Decreasing on (0,π)
c) Critical numbers: π/2, 3π/2; Extrema: Maxima at π/2, Minima at 3π/2; Increasing on (−[infinity],π/2), Decreasing on (π/2,[infinity])
d) Critical numbers: 0, π; Extrema: Maxima at 0, Minima at π; Increasing on (−[infinity],π), Decreasing on (π,[infinity])
