Suppose that f(x) = (4x + 2)^3 (x+1) then one of the points at which f(x) is increasing is x= to,

-1. -1/2, 0, -7/8

I cannot seem to figure it out, I have been doing chain rule but i just can't get the right answer if someone can help with the steps I would SO GREATLY appreciate it.

I hate math. :(

Originally Posted by Skye

Suppose that f(x) = (4x + 2)^3 (x+1) then one of the points at which f(x) is increasing is x= to,

-1. -1/2, 0, -7/8

I cannot seem to figure it out, I have been doing chain rule but i just can't get the right answer if someone can help with the steps I would SO GREATLY appreciate it.

I hate math. :(

Which steps are you having trouble with? I can help you out, but I'm not sure where to start. Are you differentiating correctly? Hint: The derivative is 2(4x+2)²(8x+7). If that's what you got, then you're on the right track.

After that, you can use an interval chart to help you figure out where the curve is increasing, then see which of those points lie within said intervals.

Edit: Damn it, ninja'd by a minute. The worst part is I took about three minutes wondering if I should help since I figured someone was going to beat me to it if I did.

1. Find the derivative (the derivative tells you the slope, if it is positive, it is increasing. If it is negative, it is decreasing)
2. Plug each values in x and if it is positive, that is your answer.

*edit*

I calculated the derivative to be 12(4x+2)^2 (x+1) + (4x+2)^3

Plugging in zero gives me 56, hence zero is the solution.

*second edit

If you do not know how to get the equation, here are the steps:

1. Recognize that (4x+2)^3 (x+1) is a chain rule!
2. We will take the derivative of the (4x+2^3) first which turns out to be 3(4x+2)^2*4
3. Remember, chain rule states take the derivative of the first TIMES the second PLUS the derivative of the second TIMES the first.
4. So, 3(4x+2)^2*4 TIMES (x+1) PLUS 1 TIMES (4x+2)^3 (note, the derivative of x+1 is equal to 1)
5. Therefore, 12(4x+2)^2 (x+1) + (4x+2)^3 is your final answer

Hope this helps..

Originally Posted by Entropy

Which steps are you having trouble with? I can help you out, but I'm not sure where to start. Are you differentiating correctly? Hint: The derivative is 2(4x+2)²(8x+7). If that's what you got, then you're on the right track.

After that, you can use an interval chart to help you figure out where the curve is increasing, then see which of those points lie within said intervals.

Edit: Damn it, ninja'd by a minute. The worst part is I took about three minutes wondering if I should help since I figured someone was going to beat me to it if I did.

...eh? I used Maple and got 12*(x+1)(4x+2)^2 + (4x+2)^3 as my derivative. Using fsolve, got -7/8, -1/2 and -1/2 as the zeros. Did you do expansion and simplification to get your derivative?

Anyway. Plug a value in between each of those points and see whether or not you get a positive or negative value. Positive = increasing, negative = decreasing.

ie. Plug -6/8 in, see what you got. Plug -1 in, see what you get. Plug 0 in, see what you get.

Wolfram is like math hamburger helper.

Beat you to it, eullwm.

You actually used maple to find the derivative!?

Originally Posted by Bhaltair

Beat you to it, eullwm.

You actually used maple to find the derivative!?

As a check to my head work, but it also helped nicely for finding the roots quickly. It's a handy tool. I especially loved using it to save time in 2ZZ3 with partial derivatives. Why solve them in MATLAB when you can solve them in Maple and copy&paste them over, formatting intact?

And hey meow, you edited your post. ):

Last edited by Bhaltair : 5 Minutes Ago at 06:05 PM.

My post was at 6:01!

Originally Posted by eullwm

As a check to my head work, but it also helped nicely for finding the roots quickly. It's a handy tool. I especially loved using it to save time in 2ZZ3 with partial derivatives. Why solve them in MATLAB when you can solve them in Maple and copy&paste them over, formatting intact?

And hey meow, you edited your post. ):

Last edited by Bhaltair : 5 Minutes Ago at 06:05 PM.

My post was at 6:01!

Ahh, you got me, looks like I didn't see your post after I did a slight edit.

Oh and eullwm, since you spoke of MATLAB, we just completed lab three for 2Z03 based on Huens and Modified Euler's method. What was the weight percentage for the best five labs last year? I heard over the summer it weighted a whopping 40% final mark.

Originally Posted by Entropy

Which steps are you having trouble with? I can help you out, but I'm not sure where to start. Are you differentiating correctly? Hint: The derivative is 2(4x+2)²(8x+7). If that's what you got, then you're on the right track.

After that, you can use an interval chart to help you figure out where the curve is increasing, then see which of those points lie within said intervals.

Edit: Damn it, ninja'd by a minute. The worst part is I took about three minutes wondering if I should help since I figured someone was going to beat me to it if I did.

I don't see why you'd use an interval chart for this problem. In less time than it takes to find your zeroes and construct the chart you could easily have just plugged the 4 options into the derivative and whichever one returns a positive number is the answer. After all, f'(x) is the slope of a tangent at f(x).

Originally Posted by Replekia

I don't see why you'd use an interval chart for this problem. In the time it takes to find your zeroes and construct the chart you could easily have just plugged the options into the derivative and whichever one returns a positive number is the answer. After all, f'(x) is the slope of a tangent at f(x).

Yeah, reading the replies after mine make me wonder why I bothered too.

It's one of the things I remembered most vividly from grade 12 Calc for some reason.

Originally Posted by Entropy

Yeah, reading the replies after mine make me wonder why I bothered too.

It's one of the things I remembered most vividly from grade 12 Calc for some reason.

I honestly avoid interval charts at all costs. They are such a huge time waster and aren't really necessary most of the time.

Originally Posted by Bhaltair

since you spoke of MATLAB, we just completed lab three for 2Z03 based on Huens and Modified Euler's method. What was the weight percentage for the best five labs last year? I heard over the summer it weighted a whopping 40% final mark.

it was like 40 and 30% I think for last year for 2Z03 and 2ZZ3. Pretty damn high. We needed it with the stupidly hard tests though( and the one easy one).

Originally Posted by BlakeM

it was like 40 and 30% I think for last year for 2Z03 and 2ZZ3. Pretty damn high. We needed it with the stupidly hard tests though( and the one easy one).

2Z03 tests weren't too bad. The exam was brutal, if I'm not mistaken. 2ZZ3 had the freebie first test, the designed-failure 2nd one and the exam was... ouch.

But yeah, 40% for 2Z03 and 30% for 2ZZ3. Or less, depending on which grading scheme you rolled.

wow thanks for the replies guys! just finished my midterm and hopefully I did okay ( Totally wish i was math person, ahh well)