Question

If g is an odd function and g'(3) = 4, what is g'(−3)?

Answer 1

if g(x) is odd then
g(-x) = -g(x)

Answer 2

so if f(3) = 4
then f(-3) = ?

Answer 3

I want to say it's simply -4 then, but I know that's not quite right

Answer 4

correct

Answer 5

why are you bumping the question? Do you not understand?

Answer 6

If g(x) is odd, what can we say about g'(x) ? :)

Answer 7

Take for example:\[\Large g(x)=x^3\]an odd function.
The derivative is an `even` function, yes? :o

Answer 8

Yeah, that makes sense. And sorry, I actually bumped it just to kind of see how everything works for this site.

Answer 9

x^3

3x^2

Answer 10

So if the derivative is an even function, it appears we need to think about the properties of even functions because that's what we're dealing with in the end, yes? :)

g'(x) is even.

Answer 11

That all makes sense. Each derivative should just be one power lower than the previous one (or in this case the function itself). However, what properties should I be looking at, for example, should I be using the Power Rule to solve this?

Answer 12

You should remember that an even function has this property:
f(x) = f(-x)

Answer 13

So if g'(x) is even:

g'(3) = ?

Answer 14

o wow nm i c

Answer 15

:o

Answer 16

sorry I thought it was g' on all of them...

Answer 17

blind:(

Answer 18

oh i see :D

Answer 19

Sorry, I've been looking at different calc stuff for the past few hours. This question was just driving me insane ha

Answer 20

do you kind of understand what's going on now caar? :x
Since g'(x) is even:

g'(3) = g'(-3)

Answer 21

Yeah, I had figured it out, thanks guys! :D

Answer 22

yay team \c:/