Stationary Points

Stationary Points

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A and B are stationary points on the curve. ( A : maximum S.P & B : is a minimum)

Intro

How to find the stationary point/s on a curve.

1. Find the first derivative/gradient of the curve in terms of x, of the curve/ equation. (The curve will be given in the form of an equation: y = ....) 

2. Knowing that at a stationary point the gradient (dy/dx)  = 0, state the line "At a stationary point dy/dx = 0"

3. Put the differentiated equation = to 0 and find x. ( this x is the x value of the coordinate of the stationary point )

Sub the x value into the equation of the curve to find the y value of the stationary point.

Points to note

* If 2 x values are found then there are 2 stationary points.

* A stationary point can have an x OR y value of 0.

* A stationary point can be a fractional coordinate.

How to find the nature of a stationary point.

Eg. 1. Find the coordinates of the stationary point on the curve.

​when x = 7

y = (7)^3 - 9(7)^2 - 21(7) + 11 = -234

when x = -1

y = (-1)^3 - 9(-1)^2 - 21(-1) + 11 = 22

Therefore the stationary points are

(7,-1) and (-1,22)

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