Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202021 Sep 2020Evening ShiftMathematicsApplication of DerivativesActual

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

Options

  1. A(a= -1 2 , b= -3 4 , c=3 )
  2. B(a= 1 2 , b= 3 4 , c=3 )
  3. C(a=1, b=2, c=3 )
  4. D(a=-1, b=-2, c=3 )

Correct answer

A. (a= -1 2 , b= -3 4 , c=3 )

Step-by-step solution

The equation of given curve is (y=a x^3+b x^2+c x+5 ) ...(i) ( ) Curve (i) passes through point (P(-2,0) ), so (-8 a+4 b-2 c+5=0 ) ...(ii) and curve (i) cuts the (Y )-axis at a point (Q ) with gradient 3, so ( . d y d x |_Q=3 ) ( 3 a x^2+2 b x+ .c |_ x=0 c=3 ) ...(iii) ( ) Point (Q ) have coordinates ((0,5) ), so curve (i) passes through (Q(0,5) ). From Eqs. (ii) and (iii), we have (8 a-4 b+1=0 ). Now, from the options (c=3, a=- 1 2 and b=- 3 4 ) Hence, option (a) 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 AP EAMCET PYQs