A tangent is a line that just touches the curve (function) at a particular point.
A function is said to be increasing at a particular x value if the gradient of the tangent at that point is positive.
A function is said to be decreasing at a particular x value if the gradient of the tangent at that point is negative.
for example
The red curve is the function that I want to refer to
The blue tangent has a positive gradient and the green tangent has a negative gradient.
All tangents on the curve where x>1 will have a positive gradients so here the function is increasing.
All tangents on the curve where x<1 will have a negative gradients so here the function is decreasing.
