If g is an odd function and g'(5) = 3, what is the value of g'(−5)? g'(−5) = ? We haven't really talked about this material in class so I'm not sure where to begin.
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What's the definition of an odd function? How about an even function? What happens when you take the derivative? – Toby Mak Sep 18 '17 at 23:36
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Can you answer this question in the case where $g(x)=3x$? – kimchi lover Sep 18 '17 at 23:36
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@Aimee Wheeler If you're satisfied with my answer, remember you can click the green tick (below the voting buttons) to accept an answer. – Toby Mak Sep 19 '17 at 02:01
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We know that the derivative of an odd function is an even function (according to this link). Since by definition, an even function has $f(-x) = f(x)$, then if $g'(5) = 3$, what is $g'(-5)$?
Toby Mak
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Let $g$ be an odd function:
1)$g(x) = - g(-x)$.
Example: $G(x) = x^3 = - G(-x)$.
2)$g'(x) = g'(-x)$ (Chain rule).
Note: $g'(x)$ is an even fct.
Example: $G'(x) = 3x^2 = G'(-x)$.
Your example:
$g'(5) = g'(-5)=3$.
Peter Szilas
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