Application of Derivatives
Prove that the function f given by f(x)=logcosx is strictly decreasing on (0,2π)and strictly increasing on (2π,π)
Let f(x)andg(x) be two differentiable functions in Randf(2)=8,g(2)=0,f(4)=10,andg(4)=8. Then prove that gprime(x)=4fprime(x) for at least one x∈(2,4)˙
A spherical iron ball 10cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50cm3/m∈ . When the thickness of ice is 5cm, then find the rate at which the thickness of ice decreases.
Points on the curve f(x)=1−x2x where the tangent is inclined at an angle of 4π to the x-axis are (0,0) (b) (3,−23) (−2,32) (d) (−3,23)
There is a point (p,q) on the graph of f(x)=x2 and a point (r,s) on the graph of g(x)=x−8,wherep>0andr>0. If the line through (p,q)and(r,s) is also tangent to both the curves at these points, respectively, then the value of P+r is_________.