Class 12

Math

Calculus

Application of Derivatives

If length of three sides of a trapezium other than base are equal to 10cm, then find the area of the trapezium when it is maximum.

$=xy+10y$

$A=x100−x_{2} +10100−x2 $

$=Ux+10 V100 −x_{2} $

$ddxA =1(100 −x_{2})+2100 −x_{2}x−10 (−2x)$

$ddxA =0$

$−100−x_{2} 100−x_{2}−x_{2}−10x =0$

$−(2x_{2}+10x−100)=0$

$−2(x_{2}+5x−50)$

$(x+10)(x−5)=0$

$x=−10$

$x=−5$

$A=xy+10y$

$15100 −25$

$=753 cm_{2}$