Question

Second derivative question?

Answer 1

Let h be a function defined for all x does not equal 0 where h(4) = -3 and the derivative is h'(x) = (x^2+x-12)/x for all x does not equal 0

Answer 2

Now there's a couple parts I have to answer.

I: Identify the intervals of increase and decrease, if any, on the graph of x.

Answer 3

Would the intervals of increase be (-4, 0) and (3, inf.) and the intervals of decrease (-inf, -4) and (0, 3) ?

Answer 4

You have to set the derivative equation to 0, because that is where the max/min will happen.

Answer 5

Than, you can check if it's increasing/decreasing using the second derivative test.

Answer 6

Yes that's what I did, I got -4, 0, and 3 as critical points

Answer 7

Wouldn't the first derivative test show whether it's increasing or decreasing?

Answer 8

No, the first derivative test shows the locations of max/min, but you can for sure do interval testing to see if it's increasing/decreasing.

Answer 9

I believe your answer should be correct.

Answer 10

I used the first derivative test and plugged in the values surrounding the critical values... if my answers look right, what do I need the second derivative test for exactly? Thanks for the help!

Answer 11

The second derivative test is just another way to find the intervals of increase/decrease. So by finding the second derivative and plugging in values where f'(x) = 0, if f''(x) < 0, it will be concave down and there will be a max, if f''(x) > 0, it will be concave up and there will be a min.

Answer 12

Oh okay, that makes sense. Does it really matter which way I do it then? If they both result in the same answer? Are there any advantages to the second derivative test?

Answer 13

Nope, there isn't really any difference. The second derivative test doesn't require you to do the interval testing, but you have to find the second derivative of a function.

Answer 14

There are two more parts to this question, I think I have the answer but I'd like someone to check them. Should I post them here or open up a new question? thanks so much for your help!

Answer 15

And by the way, I also learned this a few days ago too. Just out of curiosity, what math class are you taking?

Answer 16

You can open up a new question, so more people will see it. And no problem!

Answer 17

AP Calculus BC

Answer 18

And thanks!

Answer 19

hahah I am taking that class in my high school too!

Answer 20

Are you using the textbook Stewart Calculus: Early Transcendentals, 7th Edition?

Answer 21

Haha, yeah! Same textbook. That's funny.

How's your Calc class going?

Answer 22

Haha that's awesome. My calc class is going pretty well and it's not bad at all. You?