(5) Let f: R→R, and suppose there exist a positive integer M such that 0 < f{x) < M for all x ER. Use the limit definition of the derivative (either version) to prove that g(x) = x²f(x) + 2x is differentiable at x = 0. Do not use differentiation rules (such as power rule, product rule, ...).

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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(5) Let f: R→R, and suppose there exist a positive integer M such that 0 < f(x) < M for all x ER. Use the limit definition of
the derivative (either version) to prove that g(x) = x²f(x) + 2x is differentiable at x = 0. Do not use differentiation
rules (such as power rule, product rule, ...).
Transcribed Image Text:(5) Let f: R→R, and suppose there exist a positive integer M such that 0 < f(x) < M for all x ER. Use the limit definition of the derivative (either version) to prove that g(x) = x²f(x) + 2x is differentiable at x = 0. Do not use differentiation rules (such as power rule, product rule, ...).
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