Question

Define as Max or MIn

Answer 1

I found e^a-1 to be critical point

Answer 2

but how do i tell if it its min or max?

Answer 3

Generally you can take the second derivative, or you can test the 1st derivative at a point on either side of it. For instance if you found from the left it makes the derivative neg but on the right it is positive, that would be a max and vise versa would be a min.

Answer 4

Sorry I reversed max and min. positive -> negative would be max where the highest point is your answer.

Answer 5

Can you type out the problem? I need to work on these as well.

Answer 6

okay, for the 1st derivative test would i make it -e^a-1 and 2e^a-1?

Answer 7

I'm not sure how a is part of your function. Is it an inverse trig func?

Answer 8

f(x)=ax-xlnx

Answer 9

the derivative is a-lnx-1

Answer 10

a is just a constant

Answer 11

Hmm, so the f"(x)=-1/x. I am going through right now, but at y=0 there is a nasty little asymptote that I am trying to figure out.

Answer 12

but you eval f'' at x= e^(a-1)

Answer 13

e^(a-1) is always positive, so f'' at your critical pt -1/e^(a-1) is negative.

Answer 14

okay so its a maximum