The following figure shows the graph of a dif | vedclass

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(B) Given $g(x) = \frac{f(x)}{x}$.Taking the derivative with respect to $x$,we get:$g'(x) = \frac{x f'(x) - f(x)}{x^2}$.From the given graph of $f(x)$

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Fig $2$

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(B) Given $g(x) = \frac{f(x)}{x}$.Taking the derivative with respect to $x$,we get:$g'(x) = \frac{x f'(x) - f(x)}{x^2}$.From the given graph of $f(x)$,we observe that $f(x)$ is a concave downward function with a maximum at $x=c$ where $a At $x=c$,$g'(c) = \frac{c f'(c) - f(c)}{c^2} = \frac{c(0) - f(c)}{c^2} = -\frac{f(c)}{c^2}$.Since $f(c) > 0$ and $c > 0$ (as the interval does not contain $0$),$g'(c) This implies that the function $g(x)$ is decreasing at $x=c$. Looking at the provided options,Fig $2$ represents a curve that is concave downward and consistent with the behavior of $g(x) = \frac{f(x)}{x}$ for a positive $f(x)$ and $x > 0$. Therefore,option $(b)$ is correct.

The following figure shows the graph of a differentiable function $y=f(x)$ on the interval $[a, b]$ (not containing $0$). Let $g(x)=\frac{f(x)}{x}$. Which of the following is a possible graph of $y=g(x)$?

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