Find the Derivative Value

Calculus Level 1

Let f (x) be a function satisfying the condition f (x) = f (-x) for all real x. If f' (0) exists, then f' (0) will be?

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Vikesh Koul by Vikesh Koul , 30, India

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3 solutions

Ashish Kumar
Mar 12, 2014

Since all the even functions are symmetrical about y axis....so ,the slope should have to be zero at the origin i.e...F'(0)=0.

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Tom Engelsman
Oct 29, 2020

We have an even function f ( x ) = f ( − x ) f(x) = f(-x) for x ∈ R . x \in \mathbb{R}. Differentiating both sides yields f ′ ( x ) = − f ′ ( − x ) f'(x) = -f'(-x) , and at x = 0 x=0 we obtain f ′ ( 0 ) = − f ′ ( 0 ) ⇒ f ′ ( 0 ) = 0 . f'(0) = -f'(0) \Rightarrow \boxed{f'(0) = 0}.

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Rohullah Nikzad
Mar 29, 2014

Write a solution. since all even function are symmetrical about y axis so the slope have to be zero at the origin i.e F'(0)=0

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