Question
Prove that the exponential function ex is strictly increasing on R.
Solution
Let f (x) = ex ∴ Df = R
We are to prove that function f (x) = ex is strictly increasing. Here interval is not given. So we will prove that function ex is strictly increasing in its domain.
Now f ' (x) = ex
Three cases arise:
Case I.
Case II.
x = 0
∴ f ' (x) = ex = I > 0
Case III.
