Sect4.3_23

Some Thoughts: & the highest value for Range is 3^2 = 9 finding f ' (x) ....That is, the derivative...And finding that its sign is "Always Positive" Hence, f ' (x) Always Positive implies f (x) Always Increasing
 * We know that 3^(Stuff) is always Increasing if the (Stuff) is "Always Positive"
 * Since 3^(Positive Stuff) is always Increasing, the lowest value for Range is 3^0 = 1
 * We COULD use Calculus to "prove" f(x) as above is "Always Increasing" by

THE REASON ALL this is important, about f(x) increasing, is that the kind of short analysis done in the problem would be different if the function WASN'T monotonically increasing or decreasing. The only way we could guarantee Min/Max @ endpoints was because of the shape of the function.


 * I felt that this comment / observation was not attended to in the text **