Graph of the function g(x)=f(x)/x given graph of f(x)

Question

Since, from the given graph it seems f(a) and f(b)are equal(or approx. equal since there is no scaling given). Then f(a)/a>f(b)/b as a

Answer 1

Depending on the scale, $\frac{1}{x}$ could be close to constant on $[a,b]$, which would explain how Figure 2 could be correct.

If you calculate:

$$g'(x)=\frac{xf'(x)-f(x)}{x^2}$$

you can see that at $f$'s maximal x-value, $g'$ should be negative. This seems to rule out Fig 4. You've already ruled out Figs 1 and 3, but the reasoning does not apply to Figure 2 because there may be a difference between $g(a)$ and $g(b)$ that is too small to see.

You could also rule out Figures 1 and 3 by looking at $g'(b)$. The formula says it should be negative, but in Figures 1 and 3, it's positive.