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If f(x) =(x-x(0)) phi (x) and phi (x) is...

If `f(x) =(x-x_(0)) phi (x) and phi (x)` is continuous at `x=x_(0)` then what is `f(x_(0))` equal to ?

A

`phi (x_())`

B

`phi (x_(0))`

C

`x_(0)phi (x_(0))`

D

`2 phi (x_(0))`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that `f(x) = (x-x_(0)) phi (x)`
Differentiating w.r.t.x
`f(x) =(x-x_(0)) phi (x)+ phi(x)(1)`
putting `x=x_(0)`
`f'(x_(0))=phi(x_(0))`
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