AP EAMCET2005MathematicsContinuity and Differentiability

If f: R R is an even function which is twice differentiable on R and f^ ( )=1 , then f^ (- ) is equal to

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Correct answer

C. 1

Step-by-step solution

Let the even function be f(x)= x On differentiating w.r.t. x , we get f^ (x)=- x Again differentiating w.r.t. x , we get f^ (x)=- x at x= ^ ( )=- =1 Our assumption is true. at x=- ^ (- )=- (- )=1

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