Show that the function given by \(f(x) = e^{2x}\) is strictly increasing on \(R\).
Solution and Explanation
Then, we have:
\(x_1<x_2=2x_1<2x_2=e^{2x_1}<e^{2x_2}=f(x_1)<f(x_2)\)
Hence, f is strictly increasing on R.
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Notes on Applications of Derivatives
Concepts Used:
Increasing and Decreasing Functions
Increasing Function:
On an interval I, a function f(x) is said to be increasing, if for any two numbers x and y in I such that x < y,
⇒ f(x) ≤ f(y)
Decreasing Function:
On an interval I, a function f(x) is said to be decreasing, if for any two numbers x and y in I such that x < y,
⇒ f(x) ≥ f(y)
Strictly Increasing Function:
On an interval I, a function f(x) is said to be strictly increasing, if for any two numbers x and y in I such that x < y,
⇒ f(x) < f(y)
Strictly Decreasing Function:
On an interval I, a function f(x) is said to be strictly decreasing, if for any two numbers x and y in I such that x < y,
⇒ f(x) > f(y)
Graphical Representation of Increasing and Decreasing Functions
