Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2023MathematicsApplication of Derivatives

An enemy fighter jet is flying along the curve, given by y=x^2+2 . A soldier is placed at (3,2) wants to shoot down the jet when it is nearest to him. Then, the nearest distance is

Options

  1. A6 units
  2. B2 units
  3. C5 units
  4. D3 units

Correct answer

C. 5 units

Step-by-step solution

Let P(x, y) be the position of the jet and the solider is placed at A(3,2) . A P= (x-3)^2+(y-2)^2 As, y= (x^2+2 ) x^2=y-2 (A P)^2=(x-3)^2+x^4=z (say) d z d x =2(x-3)+4 x^3 and d^2 z d x^2 =2+12 x^2 For local points of maxima and minima aligned & d z d x =0 2(x-3)+4 x^3=0 & x=1 and d^2 z d x^2 ( at x=1)=14>0 aligned z is minimum, whe x=1, y=1+2=3 Also, minimum distance = (1-3)^2+(3-2)^2 = 5 units

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 KCET PYQs