Question: This is a Real Analysis Question. Please Prove or Disprove Let f be a function which is bounded and uniformly continuous on [0,00) and differentiable

This is a Real Analysis Question. Please Prove or Disprove

Let f be a function which is bounded and uniformly continuous on [0,00) and differentiable on (0, 00). Suppose we also know that the derivative 1" is bounded on any open interval (a, b) when a, b E [0,oo) (in particular a. and b are nite). Then 1'\" is bounded on (0,00)

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