Question

what is the range of the function y=lnx on the interval [1/e, e]?? please help and show all steps! thank you!

Answer 1

The derivate is 1/x

1/x is not equal to zero on any point in the interval, which means there are no local maximums or minimums.

Since the interval only contains positive numbers, 1/x will only tield positive results, which means it's a rising function on the interval.

So it suffices to calculate ln (1/e) and ln(e), the first will be the lowest value, the latter the highest value.

ln(1/e) = -1
ln(e) = 1

So the range of the function is [-1;1]

Answer 2

tield = yield