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get the derivative, so you know the slope of the line at x0 = 1

f(1) = 4; (1,4) we will use this to calibrate our line equation with; now we find the slope at f(1)

i see

with y = to 1 right

when y = 0 we have our x intercept, (x,0) is the x int..

0 = 8x -4
x = 4/8 = 1/2

right. man your awesome

true. well maybe since ur smart you can help with a calc problem i have.

the other maths are really applied calculus :) tell me, is the earth round or flat?

i might be able to help....my smarts come and go lol

[S] sec^2(t) dt -4 [S] dt does this make sense?

lol not really. the answer i came up with is sec t - 4t - 4

x^2

no

lets check that:....or it looks like you already did

I think:
d(tan(x)) = sec^2 did I recall correctly?

i think ur right

so would the answer be tan t - 4t

tell me, can 2 different equations have the exact same derivative?
y = 2x^2 + 6
y = 2x^2 -8

yes

right?

does that make sense?

so thats the answer

ok

P(0,0)
0 = tan(0) -4(0) + C
solve for C :)

C would b zero

thats right, but now we "know" for sure :)
so the equation is:
r = tan(t) -4t and were done :)

i like how you make sure i know where the answer is coming from. you would make a great instructor

length x width x height, right?

ok

we can factor out x right

factor out? now, we need to multiply all these together to find the equation for derive :)

ok

V = (40-2x)(40-2x)(x)
V = 1600x -160x^2 +4x^3 you wanna derive this for me?

sure i got 1600 - 320x + 12x^2

this gives me 2 numbers: x = 40/3 and x = 20/3

both of these numbers should give us an equal volume of box, but different shapes.

unless I am mistaken, and I think I am with that last one...

plug both of these into our forula stuff and see which is bigger :)

which formula

20/3 yields a bigger answer

for 40/3 we get 2014.81
.....then 20/3 it is :)

yep, for 20/3 we get 7407.41

i got 4740 for 20/3

yeah, I noticed that I punched in the wrong thing in the calculator :)

so the bigger # is the volume?

cool