Recent content by agv567

yeah i experimented and found out that the smaller you cut from the square, the larger the volume(aka larger base = larger volume). Larger altitudes give you smaller volumes. How would I find out the maximum volume using calculus work though? l

Homework Statement I am given an 8cm by 8cm piece of paper. I have to cut out a square-based pyramid out of that that gives me the greatest volume. Homework Equations I know that the volume is V = 1/3 * b^2 * h b = base h = height I know that the surface area is A = b^2 + 2bh...

The values are +-1 When I check the sign, all of them are negative So would the answer look like this? f(x) is decreasing on (negative infinity, -1) U (-1, 1) U (1, infinity)? U meaning union

Well by graphing it, all of them are negative. How would I know that you would get 2 valus for X algebraically when the derivative is never equal to zero?

Homework Statement function is (X) / (X^2 - 1)The derivative(as far as I know) is (-X^2-1) / (X^2-1)^2The Attempt at a Solution So I set it equal to zero, and I get -X^2 -1 = 0, which means X^2 = -1 This does not exist, so what would I say for the intervals? When I graph it, the function is...

But it's not X^2 + 1 = 0... It's -X^2 -1 = 0, so X^2 = -1...which does not exist. How would I tell that it was decreasing w/o a calculator?

Oh yes, I'm sorry. I had it written down correctly but I typed it incorrectly by adding a parentheses. It should be -(x^2 + 1) / (X^2-1) ^2 Now when I set it equal to zero, I get X=-1, which does not exist. How would I tell that it was decreasing over the entire domain then without graphing?

Homework Statement The equation is f(x) = (x) / (x^2 - 1)Homework Equations The equation is f(x) = (x) / (x^2 - 1) The Attempt at a Solution Well I first took the derivative, which was f'(x) = -(x^2 - 1) / (x^2 -1) ^2 I set it equal to zero to find the relative extremas, and I got -X^2 -1 =...

Yeah thanks guys, I got it. The answer is TRUE by the way, The 2nd derivative is positive throughout,

Well the question was asking if the second derivative was increasing on its entire domain... I think I'm sure this is what the first derivative looks like. http://i.imgur.com/WSu1P.jpg I'm having trouble graphing the Second though.

Homework Statement http://i.imgur.com/DQMRG.jpg Homework Equations The intervals are going by ones. The Attempt at a Solution Well for the first derivative, I'm guessing from -infinity to -1, it's a decreasing line? Also from -1 to 1...it's a constant negative line? I dunno

Thank you so much. I see my mistake now and how it confused everyone haha. I still don't understand what to do with the x^2 = -3, though.

EDIT: I'm an idiot And POI can't occur at asymptotes, right? so -1 or 1 are not POI? and x = 0...so the only POI occurs at (0,0), right? I checked with my calculator and it seems so.But what about the x^2 = -3 equation? Since it does not exist...I do nothing with it?

help...anyone ;_;

Homework Statement It asks for any Points of Inflection The second derivative is given: y'' = (2x^5 + 4x^3 - 6x) / (x^2-1)^4 Homework Equations The original function was x / (X^2 -1)The Attempt at a Solution I have set it equal to zero, and I get 2x^5 + 4x^3 - 6x = 0 I then simplified...