• 612 differentiable ⇒ continuous
ᐥIf f is differentiable at c then f is continuous at c.ᐥ Define a function g by (f(x)−f(c))/(x−c) for x≠c and f(x)ᐁx｢c｣ at x=c. ｢g(x) Ƚx￫c｣ = ｢(f(x)−f(c))/(x−c) Ƚx￫c｣ ┆f is differentiable at c┆ = f(x)ᐁx｢c｣ So g is continuous at c. g(x) = (f(x)−f(c))/(x−c ...
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