Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20249 May 2024Morning ShiftMathematicsApplication of DerivativesActual

Let C be a curve given by y(x)=1+ 4 x-3 , x 3 4 . If P is a point on C , such that the tangent at P has slope 2 3 , then a point through which the normal at P passes, is

Options

  1. A(1,7)
  2. B(3,-4)
  3. C(4,-3)
  4. D(2,3)

Correct answer

A. (1,7)

Step-by-step solution

aligned & y(x)=1+ 4 x-3 & ~d y ~d x = 4 2 4 x-3 = 2 4 x-3 & 2 4 x-3 = 2 3 & x=3 & y=4 aligned Equation of normal is aligned & y-4= -3 2 (x-3) & 2 y-8=-3 x+9 & 3 x+2 y-17=0 aligned Option (A) i.e., (1,7) satisfies above equation.

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