MHT CET202311 May 2023Morning ShiftMathematicsApplication of DerivativesActual

Value of c satisfying the conditions and conclusions of Rolle's theorem for the function f (x)=x x+6 , x [-6,0] is

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Correct answer

A. -4

Step-by-step solution

aligned f (x) & =x x+6 f ^ (x) & =x ( 1 2 x+6 )+ x+6 (1) & = x 2 x+6 + x+6 aligned Since f (x) satisfies all the conditions of Rolle's Theorem, There exists c (-6,0) such that aligned & f ^ ( c )=0 & c 2 c +6 + c +6 =0 & c +2 c +12=0 & c =-4 aligned

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