Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202419 May 2024Evening ShiftMathematicsApplication of DerivativesActual

If Rolle's theorem is applicable for the function f(x)=x(x+3) e^ - x 2 on [-3,0] . then the value of c is

Options

  1. A3
  2. B3 and -2
  3. C-2
  4. D-1

Correct answer

C. -2

Step-by-step solution

Given, f(x)=x(x+3) e^ - x 2 ,[-3,0] f^ (x)= d d x ( (x^2+3 x ) e^ -x 2 )= 1 2 (-x^2+x+6 ) e^ -x 2 Since, f(x) is satisfy Rolle's theorem so, c [-3,0] such that f^ (c)=0 aligned & 1 2 (-c^2+c+6 ) e^ -c 2 =0 c^2-c-6=0 & c=3,-2 aligned Since, c=3 [-3,0] . So, c=-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 AP EAMCET PYQs