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.
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