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JEE Main20258 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

Let the function f(x)= x 3 + 3 x +3, x 0 be strictly increasing in (- , ₁ ) U ( ₂, ) and strictly decreasing in ( ₃, ₄ ) U ( ₄, ₅ ) . Then _ i =1 ^5 _ i ^2 is equal to :-

Options

  1. A48
  2. B28
  3. C40
  4. D36

Correct answer

D. 36

Step-by-step solution

aligned & f(x)= x 3 + 3 x +3, x 0 & f^ (x)= 1 3 - 3 x^2 =0 x= 3 & f^ (x)= x^2-3 3 x^2 aligned aligned & f ^ ( x ) 0 (- ,-3) (3, ) increasing & f ^ ( x ) 0 (-3,0) (0,3) decreasing aligned _ i=1 ^5 _i^2=(-3)^2+(3)^2+(-3)^2+(0)^2+(3)^2 =36

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