Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202421 May 2024Evening ShiftMathematicsApplication of DerivativesActual

If x is real and , are maximum and minimum values of x^2-x+1 x^2+x+1 respectively then + =

Options

  1. A10 3
  2. B8 3
  3. C4 3
  4. D2 3

Correct answer

A. 10 3

Step-by-step solution

y= x^2-x+1 x^2+x+1 aligned & d y d x = (2 x-1) (x^2+x+1 )-(2 x+1) (x^2-x+1 ) (x^2+x+1 )^2 =0 & 2 x^2-2 (x^2+x+1 )^2 =0 x= 1 aligned Maximum value ( )=f(-1)= 1+1+1 1-1+1 =3 Minimum value ( )=f(1)= 1 3 + = 10 3 .

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 AP EAMCET PYQs