Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202411 May 2024Evening ShiftMathematicsApplication of DerivativesActual

The curve y=a x^3+b x^2+c x+5 touches the X -axis at (-2,0) and cuts the Y^ -axis at a point Q where its gradient is 3 , then values of a , b , c respectively, are

Options

  1. A3,- 1 2 ,- 3 4
  2. B- 3 4 ,- 1 2 , 3
  3. C- 1 2 ,- 3 4 , 3
  4. D- 1 2 , 3,- 3 4

Correct answer

C. - 1 2 ,- 3 4 , 3

Step-by-step solution

aligned & y=a x^3+b x^2+c x+5 touches X-axis at (-2,0) & 0=-8 a+4 b-2 c+5 & 8 a -4 b+2 c=5...(i) aligned Also, it cuts Y-axis at a point Q Put x=0 in the equation of curve, we get y=5 array ll & Q (0,5) & y= a x^3+ b x^2+ c x+5 & ~d y ~d x =3 a x^2+2 ~b x+ c & ( ~d y ~d x )_ Q (0,5) =3 & 3 a (0)^2+2 ~b (0)+ c =3 & c =3 array Equation (i) becomes, aligned & 8 a-4 b+6=5 & 8 a-4 b+1=0...(ii) aligned Option (C) satisfies equation (ii) Option (C) is correct

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 MHT CET PYQs