Stationary Points of x-2xsinx: 0-3pi

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In summary, a stationary point is a point on a curve where the gradient is equal to zero and the curve is neither increasing nor decreasing. To find the stationary points of a function within a given interval, the first derivative test is used. Stationary points are significant because they help identify maximum and minimum points, as well as provide information about the rate of change and concavity of the curve. A function can have more than one stationary point, and to determine if a stationary point is a maximum or minimum, the second derivative test is used, where a positive second derivative indicates a minimum and a negative second derivative indicates a maximum.
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markosheehan
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what are the stationary points of x-2xsinx in the interval of [0,3pi]
i differentiated it and let it equal to 0 . i get when i let 1-2x cosx-2sinx equal 0 i can't solve it
 
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You've differentiated correctly, and it appears to me you will have to use a numeric root finding method, such as the Newton-Raphson method to approximate the critical values. :D
 

FAQ: Stationary Points of x-2xsinx: 0-3pi

What is a stationary point?

A stationary point is a point on a curve where the gradient is equal to zero. This means that the curve is neither increasing nor decreasing at that point.

How do you find the stationary points of x-2xsinx: 0-3pi?

To find the stationary points of this function within the given interval, you would need to use the first derivative test. This involves finding the derivative of the function, setting it equal to zero, and solving for the values of x that make the derivative equal to zero. These values will be your stationary points.

What is the significance of stationary points in a function?

Stationary points are important because they can help us identify maximum and minimum points on a curve. They also provide information about the rate of change of the function at that point, as well as the concavity of the curve.

Can a function have more than one stationary point?

Yes, a function can have multiple stationary points. This means that the gradient of the curve is equal to zero at different points along the curve.

How do you determine if a stationary point is a maximum or minimum?

To determine if a stationary point is a maximum or minimum, you would need to use the second derivative test. This involves finding the second derivative of the function and plugging in the x-value of the stationary point. If the second derivative is positive, the point is a minimum. If the second derivative is negative, the point is a maximum.

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