Question

If f(x) = xe^{x(1 – x)}, then f(x)

• A. Increasing on $\left\lbrack - \frac{1}{2},1 \right\rbrack$
• B. Decreasing on R
• C. Increasing on R
• D. Decreasing on $\left\lbrack - \frac{1}{2},1 \right\rbrack$

Answer 1

Answer: (A)

Increasing on $\left\lbrack - \frac{1}{2},1 \right\rbrack$

Answer 2

f '(x) = e^{x(1 – x)} + xe^{x(1 – x)} (1 – 2x)

f '(x) = e^{x(1 – x)} (1 + x – 2x²)

f '(x) = – e^x(1–x) (2x + 1) (x – 1)

wavy curve Method sign of f '(x)

\begin{tabular} { l l l l } - & & & \ \hline & $- 1 / 2$ & + & 1 \end{tabular}

f(x) is increasing in $\left\lbrack - \frac{1}{2},1 \right\rbrack$

f(x) is decreasing in $\left( - \infty, - \frac{1}{2} \right\rbrack$Č [1, )