Find the inflection point of the function. (hint: g''(0) does not exist.) g(x) = 6x|x|

By definition of absolute value,



Differentiating once gives



As from either side, we find that , so really



Differentiating again, we find



but this time, the limit does not exist as from either side, so is undefined. However, we see that when , and when , and we know that is continuous at . This means the concavity must change at , so (0, 0) is the inflection point. (The takeaway is that inflection points *can* occur when the second derivative is undefined, but not always.)

It is the top one. the answer is -7. that is smallest