Question

The function $f(x)=\underset{0}{\overset{x^2}{\int }}\frac{t^2-1}{e^t+1}dt$ has

• A. $x=0$ as its point of inflection
• B. one maxima and one minima
• C. one maximum and two minimum
• D. two maximum and one minimum

Answer 1

Answer: (C)

$f^{\prime }(\mathrm{x})=\frac{2\mathrm{x}\left({\mathrm{x}}^4-1\right)}{{\mathrm{e}}^{{\mathrm{x}}^2}+1}$
$\mathrm{x}=0$ is the point of maxima
$\mathrm{x}=\pm 1$ is the point of minima.