Find Maximum and Minimum Values on Interval [-10, 10] for y= x^2(e^-x)

  • Thread starter Justabeginner
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In summary, the maximum and minimum values on the function y= (x^2)(e^(-x)) on the interval [-10, 10] are (0, 0) and (-10, 100*(e^10)), respectively. The critical points for this function are x=0 and x=2, and after plugging them into the function, we also get the point (2, 4/(e^2)) as a critical point. However, it is recommended to double check the point (10, 100/(e^10)) to ensure its accuracy.
  • #1
Justabeginner
309
1

Homework Statement


Find the maximum and minimum values on the function: y= (x^2)(e^(-x)) on the interval [-10, 10].


Homework Equations





The Attempt at a Solution


f'(x)= 2x*(e^(-x)) - (e^(-x)*(x^2))
f'(x)= x*e^(-x) (2- x)
Solve for zero, for critical points? I got two solutions: x=0 or x= 2

Plugging these two critical points and the endpoints on the interval back into f(x), I get:
(0, 0) - Minimum
(2, 4/(e^2) )
(-10, 100*(e^10) ) - Maximum
(10, 100/(e^10) )

Is this right? Thank you.
 
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  • #2
Justabeginner said:

Homework Statement


Find the maximum and minimum values on the function: y= (x^2)(e^(-x)) on the interval [-10, 10].


Homework Equations





The Attempt at a Solution


f'(x)= 2x*(e^(-x)) - (e^(-x)*(x^2))
f'(x)= x*e^(-x) (2- x)
Solve for zero, for critical points? I got two solutions: x=0 or x= 2
You don't "solve for zero", but I know what you mean - Set f' = 0 and solve that equation.
Justabeginner said:
Plugging these two critical points and the endpoints on the interval back into f(x), I get:
(0, 0) - Minimum
(2, 4/(e^2) )
(-10, 100*(e^10) ) - Maximum
(10, 100/(e^10) )

Is this right? Thank you.

Your max and min look OK, but check this point (10, 100/(e^10) ).
 
  • #3
Okay, I'll make sure. Thank you!
 

1. What is "Maximum/Minimum-Check Please"?

"Maximum/Minimum-Check Please" is a mathematical concept used to determine the highest or lowest value in a given set of numbers or data.

2. How is the maximum/minimum value calculated?

The maximum/minimum value is calculated by comparing each number in the set and identifying the highest or lowest value based on the given criteria.

3. What is the significance of finding the maximum/minimum value?

Finding the maximum/minimum value can provide important information about a set of data, such as the range or extremities of the values. It can also be used in decision-making processes to identify the best or worst case scenario.

4. What are some examples of when "Maximum/Minimum-Check Please" is used?

"Maximum/Minimum-Check Please" is commonly used in various industries and fields, such as finance, engineering, and statistics. It can be used to determine the highest or lowest stock prices, find the strongest or weakest materials, or identify the hottest or coldest temperatures.

5. How can errors in calculating the maximum/minimum value be avoided?

To avoid errors in calculating the maximum/minimum value, it is important to carefully review and double-check the data before performing the calculation. Additionally, using appropriate mathematical tools and techniques can help ensure accurate results.

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