Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202411 May 2024Evening ShiftMathematicsApplication of DerivativesActual

Let f (x)= x a ^2+x^2 - d -x ~b ^2+( d -x)^2 , x R where a, b, d are non-zero real constants. Then

Options

  1. Af ^ is not a continuous function of x .
  2. Bf is neither increasing nor decreasing function of x .
  3. Cf is an increasing function of x .
  4. Df is a decreasing function of x .

Correct answer

C. f is an increasing function of x .

Step-by-step solution

aligned & f (x)= x a ^2+x^2 - d -x ~b ^2+( d -x)^2 & f ^ (x)= a ^2+x^2 - x 2 x 2 a ^2+x^2 a ^2+x^2 aligned array r - (-1) b^2+(d-x)^2 + 2(d-x)^2 2 b^2+(d-x)^2 [b^2+(d-x)^2 ] = a^2+x^2-x^2 (a^2+x^2 ) a^2+x^2 - - [b^2+(d-x)^2 ]+(d-x)^2 [b^2+(d-x)^2 ] b^2+(d-x)^2 array aligned & = a ^2 ( a ^2+x^2 )^ 3 2 + b ^2 [ ~b ^2+( d -x)^2 ]^ 3 2 & 0 x R aligned f (x) is an increasing function of x .

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