question_answer 117)

Verify Rolle’s theorem for f(x) = x2 + 2x – 8 on [–4, 2] 

Answer:

f(x) = x2 + 2x ? 8              1.     Being a polynomial function, f(x) is continuous on [?4, 2]. 2.     f?(x) is derivable on (?4, 2). 3.     f(?4) = 16 ? 8 ? 8 = 0 f(2) = 4 + 4 ? 8 = 0          Since f(x) satisfies all the conditions of Rolle?s theorem. Therefore there exists at least one  such that                         f?(c) = 0                    2c + 2 + 0  c = ? 1 (?4, 2)          Hence the theorem verified.