Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2023Evening ShiftMathematicsApplication of DerivativesActual

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x . The maximum area enclosed by the park is

Options

  1. A1 2 x^2
  2. Bx^2
  3. C3 2 x^2
  4. Dx^3 8

Correct answer

A. 1 2 x^2

Step-by-step solution

Let the two sides of the triangular park having fence be x and x . Let the angle between these two sides be . The area A of the triangle is given by the formula A = 1 2 x x ( ) = 1 2 x^2 ( ) . To maximize the area A , we need to maximize ( ) . The maximum value of ( ) is 1 , which occurs when = 90^ . Substituting ( ) = 1 into the area formula, we get A_ max = 1 2 x^2 (1) = 1 2 x^2 . Answer: 1 2 x^2

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 COMEDK PYQs