f(x)= ) -7x^2+5x&forxlt 0 6x^2-4&forxgeqslant 0 According to the definition of the derivative, to compute f'(0) we need to compute the left-hand limit lim _(xarrow 0^-) which is square and the right-hand limit lim _(xarrow 0^+) which is square We conclude that f'(0) is square Note: If a limit or derivative is undefined enter undefined'as your answer.

To compute , we need to compute the left-hand limit and the right-hand limit .For the left-hand limit, we have for . Since is undefined, we can't directly compute the limit. Therefore, the left-hand limit is undefined.For the right-hand limit, we have for . Since is defined and equal to , we can compute the limit as follows: Therefore, is 0.