Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20227 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

The curve y=a x^3+b x^2+c x+5 touches X -axis at P(-2,0) , then c=

Options

  1. A4 a+5
  2. B4 a-5
  3. C5-4 a
  4. D0

Correct answer

A. 4 a+5

Step-by-step solution

y=a x^3+b x^2+c x+5 ...(i) It passes through (-2,0) 0=-8 a+4 b-2 c+5 ...(ii) aligned & d y d x =3 a x^2+2 b x+c & [ d y d x ]_ (-2,0) =12 a-4 b+c aligned According to question, [ d y d x ]_ (-2,0) =0 12 a-4 b+c=0 4 b=12 a+c ...(iii) From Eqs. (ii) and (iii), -8 a+(12 a+c)-2 c+5=0 c=4 a+5

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