Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET2007MathematicsApplication of Derivatives

The maximum area of the rectangle that can be inscribed in a circle of radius r , is

Options

  1. Ar²
  2. Br²
  3. Cr² / 4
  4. D2 r²

Correct answer

D. 2 r²

Step-by-step solution

Area of rectangle, aligned A &=2 x 2 r²-x² &=4 x r²-x² d A d x &= 4 (r²-2 x² ) r²-x² aligned For maximum or minimum put d A d x =0 x=r / 2 It can be easily checked that d² A d x² < 0 for this value of x . A is maximum for x= r 2 and the maximum value of A is given by A=4 r 2 r²- r² 2 =2 r²

Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

Consider the quadratic equation a x^2+b x+c=0 , where 2 a+3 b+6 c=0 and let g(x)= a x^3 3 + b x^2 2 +c x . Statement-I : The given quadratic equation ax ^2+ bx + c =0 has at least 2025The difference between the absolute maximum and absolute minimum values of the function f(x)=2 x^3-15 x^2+36 x-30 on [-1,4] is 2025If f(x)=x e^ x(1-x) , x R , then f(x) is 2025The angle between the curves y ^2= x and x ^2= y at the point (1,1) is 2025If the tangent of the curve 4 y^3=3 a x^2+x^3 drawn at the point (a, a) forms a triangle of area 25 24 sq.units with the coordinate axes then a = 2025If the function f(x)= x- ^2 x is defined on the interval [- , ] , then f is strictly increasing in the interval 2025If the Lagrange's mean value theorem is applied to the function f(x)=e^x defined on the interval [1,2] and the value of c (1,2) is k , then e^ k-1 = 2025If the tangent to the curve x y+a x+b y=0 at (1,1) makes an angle Tan ⁻¹ 2 with X -axis, then ab a + b = 2025 Full Application of Derivatives list All MHT CET PYQs