6. (14 pts) Let f :R→ R be a differentiable function. Suppose that 0 ≤ f' (x) ≤ f(x) for all c 
. Show that g (x) = 
is decreasing. If f vanishes at some point, conclude that f is identically zero.
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6. (14 pts) Let f :R→ R be a differentiable function. Suppose that 0 ≤ f' (x) ≤ f(x) for all c . Show that g (x) = is decreasing. If f vanishes at some point, conclude that f is identically zero.