AP EAMCET202420 May 2024Evening ShiftMathematicsApplication of DerivativesActual

A value of c according to the Lagrange's mean value theorem for f(x)=(x-1)(x-2)(x-3) in [0,4] is

Options

A2+ 2 3
B2- 16 3
C1+ 5 4
D2+ 8 3

Correct answer

A. 2+ 2 3

Step-by-step solution

f(x)=(x-1)(x-2)(x-3) in [0,4] By lagrange's mean value theorem aligned & f^ (c)= f(4)-f(0) 4-0 & (c-1)(c-2)+(c-1)(c-3)+(c-2)(c-3)= 6+6 4 & 3 c^2-12 c+8=0 c=2 48 6 =2 2 3 aligned

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