Question

Find the absolute minimum and absolute maximum values of f on the given interval.
f(x) = x − ln 3x, [1/2,2] I got -0.0986.. for the min but i got it wrong, help!

Answer 1

f(x) = x - ln 3x

f'(x) = 1 - 1/x

1 - 1/x = 0

x - 1 = 0

x = 1

Minimum is at x = 1

Answer 2

so my max is wrong too, this is how i was solving it 0.5-ln(1.5) and so on

Answer 3

Look at the graph of the function. The maximum may be at 0.5 or at 2.
Evaluate the function at those two points.

Answer 4

You evaluated the function at 0.5, but the maximum may be at another point.

Answer 5

right, and then i did the same for the min and I got-0.098 but when i typed my answer, it said it was wrong 1-ln(3)

Answer 6

For the minimum, I get it at x = 1.

Answer 7

When x = 1, f(1) = 1 - ln 3 = -0.0986

Answer 8

f(1) = 1 - ln 3 is the exact value of the minimum.

Answer 9

yeah and i used -0.0986 for the min, well i rounded so i used -0.10 and it was wrong