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MHT CET20249 May 2024Morning ShiftMathematicsApplication of DerivativesActual

If Mean value theorem holds for the function f (x)=(x-1)(x-2)(x-3), x [0,4] then the values of c as per the theorem are

Options

  1. A2 4 3
  2. B2 2 3
  3. C2 2
  4. D2 3

Correct answer

B. 2 2 3

Step-by-step solution

aligned & f (x)=(x-1)(x-2)(x-3) & f (4)=(4-1)(4-2)(4-3) & f (4)=6 & f (0)=(0-1)(0-2)(0-3)=-6 aligned Using LMVT f^ (c)= f(4)-f(0) 4-0 = 6-(-6) 4 =3 aligned & f ^ ( c )=3 ...(i) & Now, f (x)=(x-1)(x-2)(x-3) &=x^3-6 x^2+11 x-6 aligned aligned & f^ (x)=3 x^2-12 x+11 & f^ ( c )=3 & 3 c ^2-12 c +11=3 & 3 c ^2-12 c +8=0 & c = 12 48 6 =2 2 3 3 =2 2 3 aligned ...[From (i)]

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