# Math Help - Confusing homework questions HELP!!

1. ## Confusing homework questions HELP!!

1)Farmer John has 1200 feet of fencing and wishes to use it to fence a rectan-gular plot divided into two subplots as in the gure below. What are the dimensions of the plot with maximum area?

2)
Find the absolute maximum and absolute minimum values of

f
(x) = 3x4 + 4x3 12x2 + 7

on the interval [
1; 2].

2. Originally Posted by Math Phobe

1)Farmer John has 1200 feet of fencing and wishes to use it to fence a rectan-gular plot divided into two subplots as in the gure below. What are the dimensions of the plot with maximum area?

2)
Find the absolute maximum and absolute minimum values of

f
(x) = 3x4 + 4x3 12x2 + 7

on the interval [
1; 2].

For one, I cannot see the images.

For 2, you are looking for maximums and minimums. You know that wherever these occur, they must be either higher or lower than the areas around them, thus they must look like a hill or valley. Since the top of a hill, and the bottom of a valley are flat, you are looking for places where your slope is equal to zero.

So find the derivative (because this gives the formula to find the slope), and set it equal to zero (because this will tell you where the slope is zero, meaning where the slope is "flat" or where it does not change, or where it is horizontal). Find the values for x which return this, then test the areas around it to determine whether it is a "hill" or "valley" (meaning maximum or minimum") then test the two endpoints (because they could be higher or lower, even though they may not be a hill or valley. and the highest of these values will be the maximum, and the lowest will be the minimum.

3. Oh i know what ur saying but i don't know how to do the problem or start the problem at all that's why am asking it on here am totally confused about where to start! and what image are you taking about the image for the 1st question? if so that's a rectangular

4. Originally Posted by Math Phobe
Oh i know what ur saying but i don't know how to do the problem or start the problem at all that's why am asking it on here am totally confused about where to start! and what image are you taking about the image for the 1st question? if so that's a rectangular
For the first question I am talking about where it says "gure below" (presumably "figure below"), if it is there, I cannot see it. Perhaps others can see it, and can aid you.

For the second, the derivative is
$f\prime (x) = 4*3x^{4-1} + 3*4x^{3-1} -2*12x^{2-1} + 0*7x^{0-1}$

$f\prime (x) = 12x^3 + 12x^2 -24x$

Now we set it equal to zero:

$f \prime (x)=0=12x^3+12x^2-24x$

and factor

$0 = 12x(x^2 + x -2)$

factor again

$0 = 12x(x +2)(x-1)$

Now you can see that where x = 0, x=-2, x=1, the derivative will be zero.

Can you take it from here? (don't forget to take the domain into account).

5. do you by any chance know which tab to use to draw the image. I need thin line to create the box for the 1st question.