Question

33l^2-l^3-33l
Find the zeros of this polynomial function.

Answer 1

Don't you want to maximize the volume?

Answer 2

Would I be able to use the quadratic formula?

Answer 3

No quadratics only work with powers of 2. There are cubic formulas, but they take up alot of room. You could use calculus! lol. The maximum volume is 4.61*10^3 at l=21.5cm. the zeros are: 0 and 32.

Answer 4

Hm. O.k thank you for the helpful explanation! How about this:
Write an inequality that describes the possible values of x for our box problem. Remember that the y value is the volume, and that none of the dimensions can be 0 or negative.

Answer 5

(This maybe referring back to my other scenerio.)

Answer 6

3<x<30. h=3-x, so if x is 3 or less, h is zero or negative. w=30-h, so if h is 30 or more, w is zero or negative.

Answer 7

Volume is positive across all of those values too. You'll have to trust my TI-Nspire CAS for that though.

Answer 8

Thank you! I don't have the proper calculator handy :/ Do you mind?
Use your calculator to find the value of x that gives the maximum volume. Use 2nd TRACE (CALC) and choose the maximum command. Round your answer to the nearest tenth.

Answer 9

1) TI-Nspires don't work using those exact commands. 2) The maximum is posted in my second post. 3) Because I'm lazy too: V=4.61*10^3 cubic cm at x=21.5cm

Answer 10

Also, I'm sorry about the too part, it was not meant to insult you in any way.

Answer 11

Oh lol :) No it's fine! I am! :) Thank you for the help kd8cpk!

Answer 12

mathsux4real,
What is that symbol that looks like a vertical bar? Is it a lower case L?

Answer 13

Oh yeah... lowercase L=l

Answer 14

A Mathematica solution with comments is attached.

Answer 15

Wow THANKS

Answer 16

The numeric value of the roots are:\[\{\{x\to 0.\},\{x\to 1.03229\},\{x\to 31.9677\}\} \]

Answer 17

Thanks :)

Answer 18

Your welcome.