Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201824 Apr 2018Morning ShiftMathematicsApplication of DerivativesActual

If the function f(x)=x^3+2 p x^2+27 x+16 is strictly increasing for all x R , then the range of p is

Options

  1. A(- , -9 2 ) ( 9 2 , )
  2. B(- ,-9) (9, )
  3. C( -9 2 , 9 2 )
  4. D(-9,9)

Correct answer

C. ( -9 2 , 9 2 )

Step-by-step solution

aligned & f(x)=x^3+2 p x^2+27 x+16 & f^ (x)=3 x^2+4 p x+27 aligned f(x) is strictly increasing function, so f^ (x)>0 3 x^2+4 p x+27>0 Possible only when its D < 0 aligned (4 p)^2-4(3)(27) & < 0 16 p^2-4 81 & < 0 p^2- 81 4 & < 0 (p+ 9 2 ) (p- 9 2 ) & < 0 p & (- 9 2 , 9 2 ) . aligned

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