Help needed for some calculus Work!!!

Can't figure out some problems... Here's one of them

 

anyone?

 

When did they put letters in that shit

 

its fuckin psychotic

 

That's another one

 

ill help you on these later

vid chatting the gf. haha

 

lol, thanks

 

Asian to the rescue.

 

haha

 

For the first one, remember that
derivatives

e^x = e^xdx

and
e^x^2 = 2xe^x^2


the second derivative from there
f " (x) = 2 * e^x^2 * (2x^2 + 1) (chain rule)

the chain rule is the PITA here

f'(4) = plug in 4

f"(4)=...plug in 4

then use the derivatives to find the zeros, and use these as critical points; no given interval means the endpoints are infinity and negative infinity

 

you lost me lol, forgive me, but im not great at this stuff, its just a requirement lol

 

Let L be the length of the box, and let the girth equal the width AND the height of the rectangle (hence square ends)
volume = V = L*w^2
L + 4*w <= 114 inches


because of this,


L = 114 - 4*w
V = (114 - 4*w)*w^2

= 114*w^2 - 4*w^3, giving V as a function of only w.

which is what you want; since optimization relates something to something else
With the equation above, you can get dV/dW, since everything is now in terms of volume to width

so you can derive that and see what you get for w/h

 

you know how to derive, right?

 

yeah

 

when deriving e^x

the derivative is just e^x

unless there are coefficients involved

like the derivative of e^2x
is
2e^2x because of the chain rule

so the derivative of e^x^2 (x^2= 2xdx) is
2xe^x^2

 

For a guy with a glove on his head, you sure do know calculus! The glove keeps the smart in maybe...

 

I'm pretty sure I did these same problems back in calc. That was like 5 years ago though.

 

...a maximization/minimization problem... formulate "cost function", ..and find maxima or minima (peaks, valleys)...

 

Figured the other ones out thanks to all of your help... Just have 2 more I need help with