A function is said to be increasing over an interval if its first derivative is positive over that interval. i.e. the gradient of the tangents to the curve are positive, i.e sloping upwards.

A function is said to be decreasing over an interval if its first derivative is negative over that interval. i.e. the gradient of the tangents to the curve are negative, i.e. sloping downwards.

A function is said to be constant over an interval if its first derivative is 0 over that interval. i.e. the gradient of the tangents to the curve are 0, i.e. parallel to the horizontal.

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