Suppose that f and g are functions defined on [a,b] and are both differentiable at a point c ∈ [a,b]. Show that (f + g)(c) = f(c) + g(c). Show that (fg)(c) = f(c)g(c). Show that f'(c) / g'(c).
Added by Howard M.
Step 1
To show that (f+g)(x) = f(x) + g(x), we simply use the definition of function addition: (f+g)(x) = f(x) + g(x) for all x in the domain of f and g. Show more…
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