Application of Derivatives
Prove that y=(2+cosθ)4sinθ−θis an increasing function of θin [0,2π].
Let f(x)andg(x) be differentiable for 0≤x≤2 such that f(0)=2,g(0)=1,andf(2)=8. Let there exist a real number c in [0,2] such that fprime(c)=3gprime(c)˙ Then find the value of g(2)˙
The tangent to the parabola y=x2 has been drawn so that the abscissa x0 of the point of tangency belongs to the interval [1,2]. Find x0 for which the triangle bounded by the tangent, the axis of ordinates, and the straight line y=x02 has the greatest area.