question_answer 1)

Verify L.M.V. theorem for f(x) = x2 – 4x – 3 in [1, 4] 

Answer:

(x) = x2 ? 4x ? 3                   (i) f(x) is a polynomial function.          (ii)  is continuous n [1, 4]          (iii) f?(x) exists uniquely in (1, 4)          is derivable in (1, 4).          Since f(x) satisfies both conditions of L.M.V. theorem, therefore there exists at least one  such that                                              Hence the theorem is verified.