Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2021MathematicsApplication of DerivativesActual

f(x)= ( e^ 2 x -1 e^ 2 x +1 ) is

Options

  1. Aan increasing function
  2. Ba decreasing function
  3. Can even function
  4. DNone of these

Correct answer

A. an increasing function

Step-by-step solution

array l f (x)= ( e^ 2 x -1 e^ 2 x +1 ) f (-x)= e^ -2 x -1 e^ -2 x +1 = 1-e^ 2 x 1+e^ 2 x f (-x)= - (e^ 2 x -1 ) e^ 2 x +1 =- f (x) array f (x) is an odd function. Again, f ^ (x)= 4 e^ 2 x (1+e^ 2 x )² >0, x R f (x) is an increasing function.

Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

The maximum area of rectangle inscribed in a circle of diameter R is 2024Consider the function f(x)= |x-1| x^2 , then f(x) is 2024The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of radius 12 units is 2024If the angle made by the tangent at the point (x₀, y₀ ) on the curve x=12(t+ t t), y=12(1+ t)^2, 0 t 2 , with the positive x -axis is 3 , then y₀ is equal to 2024The altitude of a cone is 20 cm and its semivertical angle is 30^ . If the semi-vertical angle is increasing at the rate of 2^ per second, then the radius of the base is increasing 2024The point of inflexion for the curve y=(x-a)^n , where n is odd integer and n 3 is 2024The population p(t) at time t of a certain mouse species satisfies the differential equation d p(t) d t =0.5 p ( t )-450 . If p(0)=850 , then the time at which the population becom 2024The function f(x)= (1+x)- 2 x 2+x is increasing on 2023 Full Application of Derivatives list All BITSAT PYQs