Application of DerivativeMedium
Question
If f(x) = xex(1-x), then f(x) is
Options
A.increasing in [-1/ 2,1]
B.decreasing in R
C.increasing inR
D.decreasing in [-1/ 2,1]
Solution
Given f(x) = xex(1-x)
⇒ f′(x) = ex(1-x) + xex(1-x) (1 - 2x)
= ex(1-x) [1 + x(1 - 2x)]
= ex(1-x) (1 + x - 2x2)
= - ex(1-x) (2x2 - x - 1)
= - ex(1-x) (x - 1)(2x + 1)
Which is positive in
Therefore, f(x) is increasing in
.
⇒ f′(x) = ex(1-x) + xex(1-x) (1 - 2x)
= ex(1-x) [1 + x(1 - 2x)]
= ex(1-x) (1 + x - 2x2)
= - ex(1-x) (2x2 - x - 1)
= - ex(1-x) (x - 1)(2x + 1)
Which is positive in
Therefore, f(x) is increasing in
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