Application of Derivatives
Find the equation of the tangent to the curve y=(x−2(x−3)x−7 at the point where it cuts the x-axis.
If the tangent at any point (4m2,8m2) of x3−y2=0 is a normal to the curve x3−y2=0 , then find the value of m˙
Let P(x) be a polynomial with real coefficients, Let a,b∈R,a<b, be two consecutive roots of P(x) . Show that there exists c such that a≤c≤bandPprime(c)+100P(c)=0.
Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle is one-third that of the cone and the greatest volume of cylinder is 274πh3tan2α˙
A horse runs along a circle with a speed of 20km/h . A lantern is at the centre of the circle. A fence is along the tangent to the circle at the point at which the horse starts. Find the speed with which the shadow of the horse moves along the fence at the moment when it covers 1/8 of the circle in km/h.