Question

Help please

Answer 1

A graphing calculator is recommended.

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions W = 14 in. by L = 25 in. by cutting out equal squares of side x at each corner and then folding up the sides (see the figure).

(a) Find a function that models the volume V of the box.
V(x) = \[4x^3-78x^2+350\]
Correct: Your answer is correct.


(b) Find the values of x for which the volume is greater than 240 in3.

0.834 ≤ x ≤ 5.438

Correct: Your answer is correct.

(c) Find the largest volume that such a box can have. (Round your answer to three decimal places.)

I just need C

Answer 2

Well, let's see, first, when I tried to solve it I got this
\[ v(x) = (14 - 2x)(25- 2x)x \\
v(x) = (350 -50x - 28x + 4x^2)x \\
v(x) = 4x^3 - 78x^2 + 350x \]
which is very close to what you wrote. But I couldn't find a mistake so I just assumed you missed an x =)
Now, by the definition of the question we know that:
\[ x \ge 0 \;\;\; x \le \frac{14}{2} \;\;\; x \le \frac{25}{2} \\
0 \le x \le 7 \]
Now you have to find a maximum point in that range.
So, first calculate the derivative, find where it is 0, take the solution that fits here and prove it's the maximum with second derivative.
I would write it down, but I'm on mobile and it's a lot of typing =s
can do?