MHT CET202525 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

If f (x)= (1+x)- 2 x 2+x then f (x) is increasing in

Options

A(-1, )
B(- , )
C(0, )
D(1, )

Correct answer

A. (-1, )

Step-by-step solution

The function f(x) = (1+x) - 2x 2+x is defined for x > -1 , as both the logarithmic and rational components require this condition. The derivative is f'(x) = 1 1+x - 4 (2+x)^2 = x^2 (1+x)(2+x)^2 . Since x^2 0 and the denominator (1+x)(2+x)^2 > 0 for all x (-1, ) , we have f'(x) 0 throughout the domain. The function is therefore increasing on (-1, ) , corresponding to option A .

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 2025 The 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 2025 If f(x)=x e^ x(1-x) , x R , then f(x) is 2025 The angle between the curves y ^2= x and x ^2= y at the point (1,1) is 2025 If 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 = 2025 If the function f(x)= x- ^2 x is defined on the interval [- , ] , then f is strictly increasing in the interval 2025 If 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 = 2025 If 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