et f : [0, 1] → R be a continuous function on the closed interval [0, 1] and differentiable on the open interval (0, 1). Assume that f(0) = 0 and f’ is an increasing function on (0, 1). Show that g(x) =f(x)/x is an increasing function on (0, 1)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Let f : [0, 1] R be a continuous function on the closed interval [0, 1]

and differentiable on the open interval (0, 1). Assume that f(0) = 0 and f’ is an increasing function on (0, 1). Show that

g(x) =f(x)/x is an increasing function on (0, 1)

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