Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 7x + 14), [−4, 1]

Note that for all , so that is defined everywhere and is continuous. This means the only critical points, if any, that occur for occur when :



Now, the second derivative is



and at the critical point, we have



which means that a minimum occurs at the point .

At the endpoints of the given interval, we have




So, on the given interval, there is an absolute maximum at and an absolute minimum at .

Ithink the answer is: it is likely.