Application of Derivatives
The normal to the curve y(x−2)(x−3)=x+6at the point where the curve intersects the y-axis ,passes through the point :(21,−31) (2) (21,31) (3) (−21,−21) (4) (21,21)
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Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%.
Find the point on the curve y=(x−2)2 at which the tangent is parallel to the chord joining the points (2,0) and (4,4).
Find the equations of the tangent and normal to the hyperbola a2x2−b2y2=1. at the point (x0,y0)
If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating its surface area.
Find the equation of tangent to the curve given byx=asin3t,y=bcos3t ... (1)at a point where t=2π.
The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?
Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 34r.
Find the intervals in which the function f given by f(x)=2x3−3x2−36x+7is (a) strictly increasing (b) strictly decreasing