Chapter 3 - Sketching the curve using the derivative

3A: Increasing, Decreasing and stationary at a point

Tangents and the behaviour of a curve at a point

When a curve is sloping upwards, the tangent has a positive gradient, and y is increasing as x increases.

When a curve is sloping downwards, the tangent has a negative gradient, and y is decreasing as x increases.

Let f(x) be a function that can be differentiated at x = a.

• if f’(a) > 0, then f(x) is called increasing at x = a

• if f’(a) < 0, then f(x) is called decreasing at x = a

• if f’(a) = 0, then f(x) is called stationary at x = a