Application of Derivatives
ORAn open box with a square base is to be made out of a given quantity of cardboard of area c2square units. Show that the maximum volume of the box is 6 3c3cubic units.
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Find the equation of the normal to curve x2=4ywhich passes through the point (1, 2).
Let AP and BQ be two vertical poles at points A and B, respectively. If AP=16m,BQ=22mandAB=20m, then find the distance of a point R on AB from the point A such that RP2+RQ2is minimum.
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.
Which of the following functions are strictly decreasing on [0,2π](A) cosx (B)cos2x (C) cos3x (D) tanx
Find the equations of the tangent and normal to the parabola y2=4axat the point (at2,2at).
The slope of the normal to the curve y=2x2+3sin x at x=0is(A) 3 (B) 31 (C)−3 (D) −31
Find the equation of tangent to the curve given byx=asin3t,y=bcos3t ... (1)at a point where t=2π.
Find two positive numbers whose sum is 15 and the sum of whose squares is minimum.