Increasing and Decreasing function

Increasing Function:
A function y=f(x) is said to be increasing function in the interval (a, b) if for every x₁, x₂ ∈ (a, b) 
x₂ > x₁ => f(x₂ ) > f(x₁)
Slope of tangent at any point of such curve is always positive.
i.e., f'(x)>0

                                               ^{GRAPH OF INCREASING FUNCTION}

Decreasing Function:
A function y=f(x) is said to be decreasing function in the interval (a, b) if for every x₁, x₂ ∈ (a,b) 
x₂ > x₁ => f(x₂ ) < f(x₁)|
Slope of tangent at any point of such curve is always negative.
i.e., f'(x)<0

                                         ^{GRAPH OF DECREASING FUNCTION}