Find Critical Numbers for F(x)= x^3-12x^2 - Ash

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In summary, the function F(x) is defined as x^3-12x^2 - Ash, where x is the input or independent variable and F(x) is the output or dependent variable. Critical numbers in a function are the values of x that make the first derivative of the function equal to zero or undefined. To find critical numbers for a function, we take the first derivative of the function and set it equal to zero, then solve for x. The purpose of finding critical numbers in a function is to identify the relative maximum and minimum points, as well as analyze the behavior of the function. Critical numbers can also be used to optimize a function by finding the maximum or minimum value.
  • #1
physics_ash82
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Im supposed to find the critical numbers for the function:
F(x)= x^3-12x^2
I think I did it right I just needed some reassurance, I got
F'(x)= 3x^2-24
=3x(x-8)
=3x=0 and x-8=0

so the critcal numbers are x=0 and x=8 I think:shy: I hope someone can tell me if I did this right

Thanks
ash
 
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  • #2
yes, correct [save typo F'(x)= 3x^2-24x = 3x(x-8)]
 
  • #3
Thank you I might need more help later
:wink:
 

What is the function F(x)?

The function F(x) is defined as x^3-12x^2 - Ash, where x is the input or independent variable and F(x) is the output or dependent variable.

What are critical numbers in a function?

Critical numbers in a function are the values of x that make the first derivative of the function equal to zero or undefined. These points can help us determine the relative maximum or minimum points of the function.

How do we find critical numbers for a function?

To find critical numbers for a function, we first take the first derivative of the function and set it equal to zero. Then, we solve for x to find the critical numbers. We also need to check for any values of x that make the first derivative undefined, as these are also considered critical numbers.

What is the purpose of finding critical numbers in a function?

Finding critical numbers in a function can help us identify the relative maximum and minimum points of the function. These points can also help us analyze the behavior of the function and make predictions about its graph.

How can we use critical numbers to optimize a function?

If we are trying to optimize a function, such as finding the maximum or minimum value, we can use the critical numbers to guide us. By finding the critical numbers and evaluating the function at those points, we can determine the maximum or minimum value of the function.

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