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Find the derivatives from the left and f...

Find the derivatives from the left and from the right at x=1 (if they exist) of the following functions. Are the functions differentiable at x=1?
`f(x)=sqrt(1-x^(2))`

Text Solution

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The correct Answer is:
` = lim_(x to 1^(+)) - sqrt((1 + x)/(1- x) ) = 0 `
From (1) and (2), f' ` (1^(-)) " and " f'(1^(+)) ` are not equal .
` therefore f '(x) ` is not differentiable at x = 1 .
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