Question

If f'(x) = ln(x-2), then the graph of y = f(x) is decreasing if and only if
a) 2< x < 3
b) 0 1 e) x > 2

Answer 1

If the first derivative of a function is equal to 0, what can you discern from that?

Answer 2

x = 2 ?

Answer 3

Let's try this differently, ok, so do you know what the graph of \[ ln(x)\] looks like?

Answer 4

yes

Answer 5

Good! Okay so ln(x-2) is simply shifted 2 units to the right. And Trojan, that is incorrect.

Answer 6

Therefore, do you agree that the asymptote of f'(x) is at x=2 and has a zero at x=3?

Answer 7

i know that the slope is positive from that function

Answer 8

f'(x)=0 at x=3 so that is where f(x) will change.

Answer 9

Trojan, substitute 2.5, would you?