1. (a) Use the Mean Value Theorem to establish the following inequality
e a (x − a) < ex − e a < ex (x − a), if a < x.
1.(a)
e a (x-a) < ex - e a < e x (x-a) if a<x
Let f(x) = ex
f'(x) = ex
From Mean Value Theorem,
∀ c ∈ (a,b)
let a < x < b
so
.............................(1)
a < c < x
e a < e c < ex
e a (x-a) < ex - e a < e x (x-a) ..................from equation (1)
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