Well, today we started with two questions and worked through both for the class. Mr. K showed us how to upload pics to the other blogs, seemingly as we have RUN OUT OF SPACE on this blog =).

1)Find the global max of f(x) = 2x

^{3}-9x

^{2}+12x+2 on the interval [0, 3].

f'(x) = 6x

^{2}-18x + 12 Differentiating

= 6(x

^{2}- 3x + 2)

= 6[(x - 2)(x - 1)]

x= 2, x =1

End Points:

f(0) = 12

f(3) = 11

Critical Numbers:

f(1) = 7

f(2) = 6

From here, we can use the First Derivative test to see if there is a max or a min:

1) Draw a number line

2) Put endpoint and critical numbers in increasing order, left to right.

3) Find values in between each point on the number line and look for 'changes in sign' (maxima and minima)

2) Assume P is a positive constant f(x) = x

^{3/7}- px

^{10/7}

A) Find f'(x)

B) Find all critical number of f (answer may involve p)

C) Classify each critical number (max, min , neither)

D) Does f have a global max in it's domain? JUSTIFY.

__Solutions__

A) f'(x)= 3/7x

^{(-4/7)}- 10/7px

^{(-3/7)}

= 1/7x

^{(-4/7)}(3-10px)

= (3 - 10px)/(7x

^{4/7})

B) f'(x)= 0 when 3 - 10px = 0

3 = 10px

x= 3/(10px)

f' (x) is undefined when

7x

^{(4/7)}

x = 0

Looking at the number line, f' is positive for all x values less than 0. between 0 and 3/10p all values are also positive. All values to the right of 3/10p are negative.

C) 3/10p there is a maxima

At x = 0 there is a vertical line on the parent function.

D)

We will use: f(x) = x

^{3}- 2x

^{2}

f'(x) = x(3x-4)

+ - +

f' -----|-----|-----

0 4/3

f''(x) = 6x - 4

=2(3x-2)

second derivative test

- +

-----|-----

2/3

Inflection point at 2/3

There is a min at f (0), because

f' (4/3) = 0

f"(4/3) > 0

Here is a Short tutorial for uploading pictures =p

Upload Tutorial

1) Log into Blogger

2) Go to Pedro the Pi Rate Panda Project

3) Make a new post and click the upload button

4) Upload the file you want

5) Go back to the editor, click on "edit html" and then copy the code. Take this code and post it into your composer. Note: if your not good with html, paste the code into the compose tab so you know where your placing your image.

HW is 5.2 all odds and #2

Next scribe is...Cryyystalll =)

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