Question

Which of the following statement holds good?

• A. The function $\left(x\right)$ has an extremum point at $x=b$
• B. The function $\left(x\right)$ has an inflection point.
• C. The function $\left(x\right)$ is strictly decreasing on $(0,\infty )$
• D. The function $\left(x\right)$ is strictly increasing on $(0,\infty )$

Answer 1

The correct option is A The function $\left(x\right)$ has an extremum point at $x=b$

Given, $f\left(x\right)=b\ln x-x$
$\Rightarrow f^{\prime }\left(x\right)=\frac{b}{x}-1=0$
For extrema of $f\left(x\right)$,
$f^{\prime }\left(x\right)=0\Rightarrow x=b$
$\Rightarrow x=b$ is point of extremum