Let
f(x) =
egin{cases}
-8x^2 + 6x & ext{for } x < 0, \
5x^2 - 2 & ext{for } x ge 0.
end{cases}
According to the definition of the derivative, to compute f'(0), we need to compute the left-hand limit
lim_{x o 0^-} [ ], which is [ ],
and the right-hand limit
lim_{x o 0^+} [ ], which is [ ].
We conclude that f'(0) is undefined.
Note: If a limit or derivative is undefined, enter 'undefined' as your answer.
