Solve Stationary Points: [-5, 5]

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In summary, stationary points are points on a graph where the derivative is equal to zero and can indicate the maximum or minimum value of a function. To solve for stationary points, you need to find the derivative of the function and set it equal to zero. These points are significant because they can help find intervals of increasing or decreasing functions. Multiple stationary points can exist in a function and they have various real-life applications, such as optimizing production or determining the maximum or minimum speed of a moving object.
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Sheneron
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[SOLVED] Stationary points

Homework Statement


Does the funtion g(x) = x + sin(x) have any stationary points on the interval [-5,5], if so where?

The Attempt at a Solution


Stationary points is where there is a 0 slope so here is what I did. Just need someone to check to see if this is right.

g'(x) = 1 + cos(x)
cos(x) = -1

So for the answer I got two stationary points at pi and -pi.
 
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  • #2
Looks fine to me. Note that pi and -pi are in fact in your interval.
 
  • #3
yes, thanks.
 

1. What are stationary points?

Stationary points are points on a graph where the derivative (slope) is equal to zero. These points are important in calculus because they can indicate the maximum or minimum value of a function.

2. How do you solve for stationary points?

To solve for stationary points, you need to find the derivative of the function and set it equal to zero. Then, solve for the variable to find the x-coordinate of the stationary point. To find the y-coordinate, plug in the x-coordinate into the original function.

3. What is the significance of stationary points?

Stationary points are significant because they can indicate the maximum or minimum value of a function. They can also be used to find the intervals where the function is increasing or decreasing.

4. Can there be more than one stationary point in a function?

Yes, there can be multiple stationary points in a function. This can happen when the function has multiple maximum or minimum points, or when the function has a flat portion where the derivative is equal to zero.

5. How are stationary points used in real-life applications?

Stationary points are used in a variety of real-life applications, such as optimizing production or profit in business, finding the maximum or minimum value of a physical system, or determining the maximum or minimum speed of a moving object.

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