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For the function f(x) = x2e-x, the maximum occurs when x is equal to ____.(Answer up to the nearest integer)
Correct answer is '2'. Can you explain this answer?
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For the function f(x) = x2e-x, the maximum occurs when x is equal to _...
f(x) = x2e-x
or f'(x) = 2xe-x - x2e-x
= xe-x(2 - x)
f"(x) = (x2 - 4x + 2)e-x
Now for maxima and minima, f'(x) = 0
xe-x(2 - x) = 0
or x = 0, 2
at x= 0 f"(0) = 2(+ve)
at x = 2 f"(2) = -2e-2(-ve)
Now f"(0) = 2 and f"(2) = -2e-2 <0. Thus, x = 2is the point of maxima.
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For the function f(x) = x2e-x, the maximum occurs when x is equal to ____.(Answer up to the nearest integer)Correct answer is '2'. Can you explain this answer?
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