GATE | GATE 2017 Mock | Question 64

The value of the constant ‘C’ using Lagrange’s mean value theorem for f(x) = 8x – x² in [0,8] is:
(A) 4
(B) 8
(C) 0
(D) None of these

Answer: (A)
Explanation:

f(x) = 8x – x^2 in [0,8]
C = (0 + 8) / 2 = 4

Since, the value of ‘C’ for px^2 + qx + r (irrespective of p,q,r) defined in [a,b] using mean value theorem is mid point of the interval, i.e. C = (a + b) / 2

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