Odd or Even?
Let
f
(
x
)
be an odd, real to real, continuous and differentiable function.
Then
f
′
(
x
)
is always a/an:
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2 solutions
Great! I like your solution more than mine XD
f
′
(
−
x
)
=
d
(
−
x
)
d
f
(
−
x
)
=
−
d
x
−
d
f
(
x
)
(
f
(
x
)
as odd function)
=
d
x
d
f
(
x
)
=
f
′
(
x
)
which meets the definition of an even function.
f(x)=3x is odd then df/d(x) =3 thats is oven also >okay nice and easy
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f ( x ) = 3 x is only a special case. Though this is an easy way to duel with a multiple choices question.
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f(x)=a you sure its oven thats ask i am choosing uncorrect i think its not even
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@Patience Patience – Please don't use abbreviations/slangs as I don't understand. What is your question?
f ( − x ) = − f ( x ) ( ∵ f ( x ) is odd ) Differentiating both sides we get: ( − 1 ) f ′ ( − x ) = − f ′ ( x ) ⟹ f ′ ( − x ) = f ′ ( x ) which implies f ′ ( x ) is an Even Function .