Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202615 April 2026Morning ShiftMathematicsApplication of DerivativesActual

The co-ordinates of the point on the curve y = x x at which the normal is parallel to the line 2x - 2y = 3 are...

Options

  1. A(0, 0)
  2. B(e, e)
  3. C(e^2, 2e^2)
  4. D(e⁻², -2e⁻²)

Correct answer

D. (e⁻², -2e⁻²)

Step-by-step solution

Given curve is y = x x Differentiating with respect to x , we get dy dx = x + x 1 x = x + 1 The normal to the curve is parallel to the line 2x - 2y = 3 , which has a slope of 1 . Since the normal is perpendicular to the tangent, the slope of the tangent is -1 . Equating the derivative to the slope of the tangent: x + 1 = -1 x = -2 x = e⁻² Substituting x = e⁻² in the equation of the curve: y = e⁻² (e⁻²) = -2e⁻² The required point is (e⁻², -2e⁻²) . Answer: (e⁻², -2e⁻²)

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