Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202119 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

If f " ( x ) is a positive function for all x ∈ R , f ' ( 3 ) = 0 and g ( x ) = f tan 2 ( x ) - 2 tan ( x ) + 4 ) for 0 < x < π 2 , then the interval in which g ( x ) is increasing is

Options

  1. Aπ 6 , π 3
  2. B0 , π 4
  3. C0 , π 3
  4. Dπ 4 , π 2

Correct answer

D. π 4 , π 2

Step-by-step solution

f ' ' x is a positive function for all x ∈ R , ⇒ f ' x is an increasing function for all x ∈ R As, f ' 3 = 0   ⇒   f ' x   > 0   , for all x > 3 . . . 1 Now, we have a function g ( x ) = f tan 2 ( x ) - 2 tan ( x ) + 4   ⇒ g ' x = f ' tan 2 ( x ) - 2 tan ( x ) + 4 × d tan 2 ( x ) - 2 tan ( x ) + 4 d x Consider, g x is an increasing function, then g ' x > 0 ⇒ g ' x = f ' tan 2 ( x ) - 2 tan ( x ) + 4

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