Question

1) If f is even a f ' (22) = 5, what is f ' (-22) ?

2) If f is any even function, and f ' (0) exists, what is f ' (0) ?

**don't know where to start on either of the problems.:(

please explain? thank you!!! :)

Answer 1

Perhaps the fundamental theorem of calc would help.

Answer 2

what would that be? I can't remember which one it is :/

Answer 3

However, I have a suspicion that the derivative of an even function is an odd function.

Answer 4

1) f'(-22)=-5
2) f'(0) = 0

for 1) use this : f'(x)=-f'(-x) for an even function
for 2) consider any even function, like x^2 and figure it out

Answer 5

ohhh i see :)

and from there, just plug in and solve right? :o

Answer 6

If \(f(x)\) is even, then \[
f(x) = f(-x)
\]Differentiate both sides and then \[
f'(x) =-f'(-x)
\]

Answer 7

Simple proof. Thank god.

Answer 8

By the way, I used chain rule where \(g(x) = -x\) in case you're wondering.

Answer 9

ahh okay awesome!! thank you both!! @ali_rami1990 @wio :)

and lol yes, thank the lords :P

Answer 10

anytime