Question

Find the critical points and the intervals on which f (x) = x^2-5x+6/ x^2?
increases/decreases. Hence decide whether each critical point represents a
minimum, a maximum or neither. ??

Answer 1

Can you calculate the first derivative? Use quotient rule.

Answer 2

yes done it all out and think it has one critical point at -0.0417 at local min but not sure am i right . i got 1st & 2nd derivative then got x =2.4 subed it back in nd got that answer but am not sure am i correct

Answer 3

I got a critical point min at x = 2.4. I didn't bother with the second derivative and I just noticed that the first derivative goes from - to + at x = 2.4, so that one's for sure.

Answer 4

Aslo, looks like the function increases for x<0 and x > 2.4. Decreases in 0 < x < 2.4

Answer 5

yes i think it has 1 critical point which is a minimum but i was just trying to see was i right as was a bit unsure

Answer 6

No, you're right. f(x) also goes to infinity on left and right-hand of x going to 0

Answer 7

cheers

Answer 8

Horizontal asymptote of f(x) at 1 for x going to infinity. You, too on the cheers! I'm right now drinking Octoberfest beer.

Answer 9

So, just one relative min. No max.

Answer 10

yes i think so , hopefully this is the right answer for my problem sheet !!!

Answer 11

I graphed it and yes, it just has this one min. No max.

Answer 12

@tcarroll010 are you in Germany?

Answer 13

Octoberfest is big in Bavaria.

Answer 14

No, I'm in the U.S. I'm just one of the few with good, European beer taste, lol. :-)

Answer 15

Great, I am in U.S. also, but did spend 3 years in Bavaria near Bad Toelz,Germany. (Thanks to our U.S. Army)