#stationary points

[precisestudy]

Simple understanding of Stationary Points1.

Stationary points are points on a curve where the function is neither increasing or decreasing. That is, f(x) is not changing at the stationary point. We call it stationary because when we envision an object moving along the curve f(x), the object stops there. The object will be stopping at that point. A stationary point on a function f(x) is a point where the derivative of f(x) is equal to 0.…

Simple understanding of Stationary Points1.

[drcyrus]

Understanding Stationary Points: Definition and Identification

Stationary points on a curve are where the function is neither increasing nor decreasing. They occur where the derivative of the function is 0. Depending on the change in gradient, stationary points can be classified as maximum or minimum points. Identify

Stationary points are points on a curve where the function is neither increasing or decreasing. That is, f(x) is not changing at the stationary point. We call it stationary because when we envision an object moving along the curve f(x), the object will be stopping at that point. A stationary point on a function f(x) is a point where the derivative of f(x) is equal to 0. At the stationary point,…

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[glassofsweetsalicineester]

Stationary points poll made me so happy

It's a shame tumblr doesn't allow forever-polls :( But I love those 36+ people who responded to that silly poll, filling my heart with giggles over degenerate source/sink and spirals and saddle appreciators (other equilibrium states are also cool, these are just notable)

[glassofsweetsalicineester]

What stationary point are you?

Saddle

Center

Sink

Source

Degenerate sink

Degenerate source

Spiral sink

Spiral source

Line of stable fixed points

Line of unstable fixed points

Secret option (field of fixed points)

Voting ended onMay 16, 2024

[iamrevisinghonest-gcse]

Stationary Points

A stationary point is a point on a graph where the gradient is zero.

There are three types of stationary points:

Minimum points -- these are found at the bottom of a positive parabola

Maximum points -- these are found at the top of a negative parabola

Points of inflection -- these are found in the middle of a cubic graph.

We can use differentiation (δy/δx) to find stationary points.

Method:

Find δy/δx

Solve δy/δx = 0

Find the y co-ordinate by substituting the x values into the original equation.

Example:

A curve has the equation y = x3 – 6x2 – 36x. Find the co-ordinates of any stationary points on the curve.

δy/δx = 3x2 – 12x – 36

3x2 – 12x – 36 = 0

x = 6 or -2

y = x3 – 6x2 – 36x

y = 63 – (6 x 62) – (36 x 6)    = -216

y = (-2)3 – (6 x (-2)2) – (36 x (-2))    = 40

(6, -216) and (-2, 40)

We can use the second differentiation (δ2y/δx2) to classify stationary points.

Method:

Find the second differentiation and solve for the given values - If δ2y/δx2 < 0, the point is a maximum point - If δ2y/δx2 > 0, the point is a minimum point - If δ2y/δx2 = 0, the point is a point of inflection

[mathsmathsmaths]

[mathsmathsmaths]