What are the Maximum and Minimum Values of the Function s(t) = 1+2t-8/(t^2+1)?

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In summary, a maximum and minimum in calculus refer to the highest and lowest points on a graph or function, respectively. To find these points, the derivative of the function is taken and set equal to zero, allowing for the x-value of the maximum or minimum to be determined. The significance of finding these points lies in understanding the behavior of the function and being able to optimize systems or solve problems. There is a difference between local and global maximum/minimum points, with the former referring to a specific interval and the latter referring to the entire domain of the function. While calculus can be used to find the maximum or minimum of any continuous function, some may require more advanced techniques.
  • #1
thomasrules
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I have to find the Max and Minimum in this question.
I'm stuck because I can't find t.

s(t)= 1+2t-8/(t^2+1)

I've got:

s prime(t)= 16t(t^2+1)^-2 +2

Thanks
 
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  • #2
ok so I assume your equation is [tex] s(t) = (2t+1) - \frac{8}{t^2+1} [/tex] Is this correct? Then [tex] \frac{ds}{dt} = 2 - \frac{16t}{(t^2+1)^2} [/tex] Then [tex] t = 0 [/tex]
 
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  • #3
sorry wrong equation:

(1+2t)-(8/t^2+1)
 

1. What is the difference between a maximum and a minimum in calculus?

In calculus, a maximum refers to the highest point on a graph or function, while a minimum refers to the lowest point on a graph or function. This can be visualized as the peak or valley of a curve.

2. How do you find the maximum or minimum of a function using calculus?

To find the maximum or minimum of a function using calculus, you must first take the derivative of the function and set it equal to zero. Then, solve for the x-value that makes the derivative equal to zero. This x-value will correspond to the maximum or minimum point on the function.

3. What is the significance of finding the maximum or minimum of a function?

The maximum or minimum of a function can provide important information about the behavior and critical points of the function. It can also be used to optimize a system or find the best solution to a problem.

4. What is the difference between a local maximum/minimum and a global maximum/minimum?

A local maximum or minimum refers to the highest or lowest point on a specific interval of a function, while a global maximum or minimum refers to the highest or lowest point on the entire domain of the function.

5. Can calculus be used to find the maximum or minimum of any type of function?

Yes, calculus can be used to find the maximum or minimum of any continuous function. However, some functions may require more advanced techniques such as partial derivatives or multivariable calculus to find the maximum or minimum.

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