Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2009MathematicsApplication of Derivatives

The minimum value of 27^ 2 x 81^ 2 x is

Options

  1. A-5
  2. B1 5
  3. C1 243
  4. D1 27

Correct answer

C. 1 243

Step-by-step solution

Let f(x)=27^ 2 x 81^ 2 x =3^ 3 2 x+4 2 x =3^ 5 ( 3 5 2 x+ 4 5 2 x ) Let 3 5 = 4 5 = then f(x)=3^ 5( 2 x+ 2 x) =3^ 5( ( +2 x)) For minimum value of given function, ( +2 x) will be minimum, ie, ( +2 x )=-1 f ( x )=3^ 5(-1) = 1 243

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 KCET PYQs