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anonymous
 one year ago
Recall that a function 'f' is said to be even if f(x) = f(x) for all x. Suppose we are given an even realvalued function 'f' which is differentiable for all values of x, and suppose furthermore that f(c) = 1, and f'(c) = 5 at some point c > 0. Use the definition of the derivative to find f'(c). State the value of f'(0), giving reasons for your answer.
anonymous
 one year ago
Recall that a function 'f' is said to be even if f(x) = f(x) for all x. Suppose we are given an even realvalued function 'f' which is differentiable for all values of x, and suppose furthermore that f(c) = 1, and f'(c) = 5 at some point c > 0. Use the definition of the derivative to find f'(c). State the value of f'(0), giving reasons for your answer.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Definition of f' in x=c is: \(f'(c)=\lim_{h\to 0} \dfrac{f(c+h)f(c)}{h}\) What you can do now, is replace c with c in this definition.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ah okay, so like: f'(c) = lim f(c + h)  f(c) h>0 h

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, \(f'(c)=\lim_{h \rightarrow 0}\dfrac{f(c+h)f(c)}{h}=\lim_{h \rightarrow 0}\dfrac{f(ch)f(c)}{h}=\) \(\lim_{h \rightarrow 0}\dfrac{f(ch)f(c)}{h}=\lim_{h \rightarrow 0}\dfrac{f(c+h)f(c)}{h}=f'(c)\)
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