1.

Verify Lagrange's Mean Value Theorem in interval [0,4), where function f(x) = (x - 1) (x - 2) (x - 3).

Answer»

Given function f(x) = (x - 1) (x - 2) (x - 3)

Hence, f(a) = (-1) (-2) (-3) = 6

∴ f(0) = 6

∵ Given function is polynomial Hence function is.

(i) Continuous in closed interval (0,4)

(ii) Differentiable in open interval (0, 4) 



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