Question

Find the absolute maximum and absolute minimum values of f on the given interval. (Round all answers to two decimal places.)
f(x) = x - ln(8x)
[0.5, 2] Find the absolute maximum and absolute minimum values of f on the given interval. (Round all answers to two decimal places.)
f(x) = x - ln(8x)
[0.5, 2] @Mathematics

Answer 1

Erm, so I suppose i start with
\[f'(x)=1-1/x\]

And...now i'm stumped...

Answer 2

take the derivative of the function. set it equat to zero and solve for x. this gives local max and min x values. to find the y's plug those x s back into ito the original function

Answer 3

don't forget to plug the 0.5 and 2 into the original functiontoo. the smallest f(x) will be the absmin and the biggest will be abs max

Answer 4

Okay so

f'x=1-1/1 =0
x=1

So I plug that back into original function?
f(x)=1-ln(8)????

Answer 5

Wait, why would i plug in .5 and 2. The abs min or max could be 1.232 for all I know?

Answer 6

yes. also the endpoints of the interval. of the all the f(x) the largest would be the max and the smallest would be the min

Answer 7

Yes to what? I don't see what you are trying to say.

Okay so I plugged x=1 into the original function like you said. f(x)=1-ln(8). What in the world do i do now? I don't know what ln(8) is without a calculator...

Answer 8

ln8 = 2.07

Answer 9

Did you figure that out in your head...? I'm supposed to be able to do all of this without a calculator.

Answer 10

But regardless, 1-2.07=-1.07
Okay, that was correct! Wow... So how do I find the max now?

Answer 11

but the ln function increases so you know ln 4< ln8<16

Answer 12

the largest solution is the max

Answer 13

Got it, -.77

Okay so basically I just have to actually picture what the function looks like in my head.

Thanks!

Answer 14

yes you must include the endpoints because they can be actually the min or max and the derivative only gives you a relative max or min