Application of Derivatives
If p and q are positive real numbers such that p2+q2=1, then the maximum value of (p+q) is
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Find the condition if the equation 3x2+4ax+b=0
has at least one root in (0,1)˙
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˙
If the tangent at (1,1)
meets the curve again at P,
then find coordinates of P˙
In the curve xayb=Ka+b
, prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).
Tangent of an angle increases four times as the angle itself. At what rate the sine of the angle increases w.r.t. the angle?
Show that the straight line xcosα+ysinα=p touches the curve xy=a2, if p2=4a2cosαsinα˙
radians, then find the approximate value of cos6001prime˙
Let y=f(x) be drawn with f(0)=2 and for each real number a the line tangent to y=f(x) at (a,f(a)) has x-intercept (a−2). If f(x) is of the form of kepx thenpk has the value equal to