Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2016MathematicsApplication of Derivatives

If the curve y=2 x³+a x²+b x+c passes through the origin and the tangents drawn to it at x=-1 and x=2 are parallel to the X -axis, then the values of a, b and c are respectively,

Options

  1. A3,-12 and 0
  2. B-3,12 and 0
  3. C-3,-12 and 0
  4. D12,-3 and 0

Correct answer

C. -3,-12 and 0

Step-by-step solution

y=2 x³+a x²+b x+c...(i) Since, it passes through (0,0) , 0=2(0)+a(0)+b(0)+c aligned c &=0 ...(ii) d y d x &=6 x²+2 a x+b aligned Since, tangents at x=-1 and x=2 are parallel to X -axis. d y d x =0 At aligned x &=-1 6(-1)²+2 a(-1)+b &=0 6-2 a+b &=0...(iii) aligned At x=-2 So, aligned 6(2)²+2 a(2)+b &=0 24+4 a+b &=0...(iv) aligned By solving Eqs. (iii) and (iv), we get a=-3, b=-12 Hence, a=-3, b=-12, c=0

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 COMEDK PYQs