Class 12

Math

Calculus

Application of Derivatives

ORAn open box with a square base is to be made out of a given quantity of cardboard of area$c_{2}$square units. Show that the maximum volume of the box is $63 c_{3} $cubic units.

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Find the equation of the normal to curve $x_{2}=4y$which 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 $RP_{2}+RQ_{2}$is 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 $y_{2}=4ax$at the point $(at_{2},2at)$.

The slope of the normal to the curve $y=2x_{2}+3$sin x at $x=0$is(A) 3 (B) $31 $ (C)$−3$ (D) $−31 $

Find the equation of tangent to the curve given by$x=asin_{3}t,y=bcos_{3}t$ ... (1)at a point where $t=2π $.

Find two positive numbers whose sum is 15 and the sum of whose squares is minimum.