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domyy
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Homework Statement
Find extrema and points of inflection (then graph it).
f(x) = x2e-x
Homework Equations
The Attempt at a Solution
So, for f'(x) = xe-x(2-x)
Critical point(s):
f'(x) = 0
2-x = 0
x= 2
I have a question before continuing. Will my critical point include 0 besides 2?
I still have doubts about whether 0 is always part of the critical points because my prof., when working on a similar problem, stated that only the number found was the critical point and didn't use zero. He said that e-x cannot be equal to zero. Meaning he used 2 to find the extrema. What he did was using test numbers between 2 to see where it was increasing and decreasing (THAT if I didn't miss any step while copying it - I tend to rush a little when copying the notes on the board since he writes a lot).
However, with this problem, my book seems to use 0 as the other point to find extrema. For instance, when substituting 2 and 0 back into the original function, I'll have (2, 4e-2) and (0,0). Being the first , the MAX and the last, the MIN extrema.
Does that mean that 0 was the other critical point?
Meaning, will 0 ALWAYS be part of the critical point and be used to find the MIN/MAX extrema?
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