f(x)= ) 7x-8x^2&forxlt 0 7x^2+7x&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.The left-hand limit is the limit of the derivative of the function as approaches from the left side. In this case, the function is defined as for . Taking the derivative of this function, we get . Evaluating this at , we get .The right-hand limit is the limit of the derivative of the function as approaches from the right side. In this case, the function is defined as for . Taking the derivative of this function, we get . Evaluating this at , we get .Since the left-hand limit and the right-hand limit are both equal to , we conclude that .