Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2010
Exam
BITSAT
Year
2010
Subject
Mathematics
Chapter
Application of Derivatives

BITSAT 2010 · Mathematics · Application of Derivatives

The function ( f(x)= x- 4 x ) is strictly decreasing on

The function (f(x)=tan⁡x−\mathrm{f}(\mathrm{x})=\tan \mathrm{x}-4 x\mathrm{x}) is strictly decreasing on

Options

  1. A((−π3,π3)\left(-\frac{\pi}{3}, \frac{\pi}{3}\right))
  2. B((π3,π2)\left(\frac{\pi}{3}, \frac{\pi}{2}\right))
  3. C((−π3,π2)\left(-\frac{\pi}{3}, \frac{\pi}{2}\right))
  4. D((π2,π)\left(\frac{\pi}{2}, \pi\right))

Correct answer

A. ((−π3,π3)\left(-\frac{\pi}{3}, \frac{\pi}{3}\right))

Step-by-step solution

(f(x)=\tan x-4 x \Rightarrow f^{\prime}(x)=\sec ^2 x-4) When (−π3<x<π3,\frac{-\pi}{3} \lt \mathrm{x} \lt \frac{\pi}{3},1 \lt \sec x<\mathrm{x} \lt2) Therefore, (1 \lt \sec ^2 x \lt 4) (\Rightarrow-3 \lt \left(\sec ^2 x-4\right) \lt 0) Thus,for(−π3<x<π3,\mathrmf′(x)<for (\frac{-\pi}{3} \lt \mathrm{x} \lt \frac{\pi}{3}, \mathrmf^{\prime}(\mathrm{x}) \lt0) Hence, (f\mathrm{f} is strictly decreasing on ((−π3,π3)\left(\frac{-\pi}{3}, \frac{\pi}{3}\right)
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 BITSAT 2024Consider the function f(x)=(|x-1|)/(x^2) , then f(x) is BITSAT 2024The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of… BITSAT 2024If the angle made by the tangent at the point (x_0, y_0) on the curve x=12(t+ t t)… BITSAT 2024The altitude of a cone is 20 cm and its semivertical angle is 30^ ^ ∘ . If the… BITSAT 2024The point of inflexion for the curve y=(x-a)^n , where n is odd integer and n ≥ 3 is BITSAT 2024The population p(t) at time t of a certain mouse species satisfies the differential… BITSAT 2024The function f(x)= (1+x)-(2 x)/(2+x) is increasing on BITSAT 2023If f(x)= x, g(x)= 2 x, h(x)= 3 x and I(x)= x , then which of the following option is… BITSAT 2023The interval in which the function f(x)=(4 x^2+1)/(x) is decreasing is : BITSAT 2023The curve given by x+y=e^ x y has a tangent parallel to the Y-axis at the point BITSAT 2023The function f(x)= ^ -1 ( x+ x) is an increasing function in BITSAT 2023A running track of 440 ft is to be laid out enclosing a football field, the shape of… BITSAT 2022A spherical balloon is filled with 4500 π cubic meters of helium gas. If a leak in the… BITSAT 2022The points at which the tangent passes through the origin for the curve y=4 x^ 3 -2 x^ 5… BITSAT 2021If the radius of a sphere is measured as 9 cm with an error of 0.03 cm , then find the… BITSAT 2021 Full Application of Derivatives list Application of Derivatives JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs