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Locate Absolute Extrema

  • Thread starter domyy
  • Start date
  • #26
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Thank you for your reply!
I am having trouble with the exercise f(x) = 3x^2/3 - 2x ; (-1,1)
You need parentheses around the exponent. This is what you wrote:
f(x) = ## \frac{3x^2}{3} - 2x##

This is what I think you meant
f(x) = 3x2/3- 2x

Without using LaTeX or the HTML tags that I used, you can write it this way:
f(x) = 3x^(2/3) - 2x
I already found (-1,5) and (1,1) by plugging the intervals back into the function.
But -1 and 1 aren't in the domain.
But I have f'(x) = 2x^-1/3 -2 = 0
Again, you need parentheses. This is f'(x) = 2x^(-1/3) - 2
Now, I am having trouble finding the answer. I found 1 which would give me (1,1).

However, the answer should be MIN (0,0) and MAX (-1,5). And I don't understand it.
From an earlier post:
Maxima or minima can occur at these places:
1. Numbers in the domain at which the derivative is zero.
2. Numbers in the domain at which the original function is defined, but the derivative is undefined.
3. Endpoints of the domain.
 

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