Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET2019Morning ShiftMathematicsApplication of DerivativesActual

The slope of normal to the curve x = t and y = t - 1 t at t = 4 is …

Options

  1. A- 17 4
  2. B4 17
  3. C- 4 17
  4. D17 4

Correct answer

C. - 4 17

Step-by-step solution

K e y I d e a F i r s t l y f i n d d y d x = d y l d t d x l d t , t h e n U s e s l o p e o f n o r m a l = - 1 d y d x We have, x = t and y = t - 1 t Now d x d t = 1 2 t , d y d t = 1 + 1 2 t - 3 2 ∴ d y d x = d y d t d x d t = 1 + 1 2 t 3 / 2 1 2 t = 2 t 1 + 1 2 t - 3 2 = 2 t 1 + 1 2 t 3 / 2 = 2 t 3 / 2 + 1 t A t t = 4 , d y d x = 2 4 3 / 2 + 1 4 = 17 4 ∴ Slope of normal at t = 4 , - 1 d y d x = - 4 17

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