A projectile is launched from ground level with an initial velocity 0 at an angle ,

A projectile is launched from ground level with an initial velocity ν₀ at an angle θ, where 0 ≤ θ ≤ π/2. Its horizontal range is R = (2v²₀/g) sinθ cos θ, where g = 32 ft/s² with  ν₀ in ft/s, and g = 9.8 m/s² with ν₀ in m/s. Calculate dR/dθ. The maximum range occurs where dR/dθ = 0. Show that that occurs at θ = π/4 and that the maximum range is v²₀/g.