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Increasing and Decreasing function:

Increasing function:

A function f(x) is called a increasing function in I

if x < x ⇒ f (x ) ≤ f(x ) for all x ,x ∈ I
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Strictly increasing function:
A function f is called a Strictly Increasing function in I
if x < x ⇒ f(x ) < f x for all x ,x ∈ I
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Decreasing function:
A function f(x) is said to be decreasing function in I

if x < x ⇒ f(x ) ≥ f(x ) for all x ,x ∈ I
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Strictly decreasing function :
A function f(x) is said to be Strictly decreasing function in I
if x < x ⇒ f(x ) >f(x ) ) for all x ,x ∈ I
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Using derivate how to test increasing and decreasing function

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i) If f (x) > 0 then f(x) is st.increasing.

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ii) If f (x) ≥ 0 then f(x) is increasing.
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iii) If f (x) < 0 then f(x) is st.decreasing.

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iv) If f (x ≤ 0 then f(x) is decreasing.

Example: - Show that f(x) =2x + 1 is the function strictly increasing on R.

Ans: - Given that f(x) =2x + 1

Letx , x ∈ R and x < x
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⇒ 2x < 2 x ⇒ 2 x + 1 < 2 x + 1
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