Need Help on some Calc Work badly

[mjmcgove]

i struggle with math a lot, so these are giving me a good amount of trouble

 

[mjmcgove]

can anyone help?

 

[serds]

What have you done so far?

 

[mjmcgove]

What have you done so far?

out of those 2 i am at a complete loss, havent made any progress whatsoever

 

[serds]

Ok, You need the chain rule for this one.
f'(x)=4e^(-x^2)*(-x^2)'=4e^(-x^2) * ( -2x) = -8xe^(-x^2)

 

[mjmcgove]

Ok, You need the chain rule for this one.
The derivative is
f'(x)=

the pictures dont work for me?

 

[MarkFL]

For the second problem, have you found the objective function and the constraint?

 

[mjmcgove]

For the second problem, have you found the objective function and the constraint?

no, i havent gotten anywhere with either problem

 

[serds]

The graph is increasing, where f'(x)>0 and decreasing, where f'(x)<0.

 

[mjmcgove]

still stuck on the first one, could you give me a step by step... I'm not great with this stuff, as you can tell

 

[serds]

f''(x)= -8*(xe^(-x^2))'= -8 [(x)'*e^(-x^2) + x*(e^(-x^2))']=
-8[1*e^(-x^2)+ e^(-x^2)*(-x^2)'*x]=
-8[-(x^2)'*x*e^(-x^2)+e^(-x^2)]=
-8(e^(-x^2)- (2x^2)*e^(-x^2))

 

[MarkFL]

no, i havent gotten anywhere with either problem

If the length of the edges on the square end is \(\displaystyle x\) and the length of the box is \(\displaystyle \ell\) (all measures in inches) then:

The volume of the box (the objective function) is:

\(\displaystyle V=x^2\ell\)

and the constraint imposed by the postal service is:

\(\displaystyle \ell+4x=114\) (letting the sum of the length and girth be the maximal value)

Now, you most likely will want to solve the constraint for \(\displaystyle \ell\), then substitute into the objective function so that you will then have the volume as a function of one variable. At this point you want to differentiate with respect to this variable, equate the derivative to zero to find the critical value(s), then determine which, if any, are at a local maximum.

Once you find the critical value associated with the maximum, then evaluate \(\displaystyle \ell\) and \(\displaystyle V(x)\) at this critical value to answer the questions asked, that is, to find the dimensions of the box meeting the restrictions and having the largest volume, and the measure of this largest volume.

Let us know if you get stuck during the process of applying these steps to the problem.