Recent content by Pondera

Lane, I divided 3x^2+6x by two and got y'=3/2x^2+3x. By power of x, I take it you mean power of 2? I neglected to put that in here, but it is on my scratch paper, I appologize. I don't see where the arithmetic is flawed? I certainly believe that that is likely not the equation/form that I...

Homework Statement Find an equation of the tangent line to this curve at the point (1, -2). Homework Equations The Attempt at a Solution 2y' = 3x^2+6x y' = 3x^2+6x y'=3/2x^2+3x y+2=3(x-1) y+2=3x-3 y=3x-5

WOOO! It was right! Thank you very much, jgens and gabba.

Yeah, it should be divided by our multiplied by (1/2xy). I'm not sure why I did that. :P The rest of it looks okay though?

I wasn't using the product rule at all. Thank you for that! Haha. I tried it again and got: Line by line: 7= cos(xy^2)(y^2+2xyy') 7/ cos(xy^2) = (y^2+2xyy') 7/ cos(xy^2) - y^2 = 2xyy' (7/ cos(xy^2) - y^2)(2xy) = y'

Homework Statement Homework Equations The Attempt at a Solution

Homework Statement If a tank holds 3500 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as the following. V = 3500 (1-t/50)^2 0 </=t<=50 Find the rate at which water is...

Thank you very much! I'm not sure why I had such a hard time conceptualizing what that question was asking, but your hints were correct and I got it.

Homework Statement If the tangent line to y = f (x) at (9,7) passes through the point (0,6), find the following. (a) f (9) (b) f ' (9) Homework Equations f '(x) = f(x+h) - f(x)/h ? The Attempt at a Solution I really have no idea how to even begin going about this one, so a...

Isn't f'(a) just -6a^2+8a? Thank you again for the help and the suggestions on formatting! Edit: Apparently it is, and I was able to get the other parts of the problem (finding the equation of the tangent line given a point) easily enough. I really can't thank you enough!

1. -2x^3+4x^2-6x^2h-6xh^2+8xh-2h^3+4h^2+4 2. -6x^2h-6xh^2+8xh-2h^3+4h^2 3. -6x^2-6xh+8x-2h^2+4h 4. -6x^2+8x

This is the only formula we've learned so far, though I'm sure we'll be learning differentiation formulas shortly. After taking f(x+h)-f(x)/h I came up with -6x^2-6xh-2h^2-4x^2/h-4/h, then plugging in 0 for h to take the lim h->0 I come up with -6x^2. I have a couple more sections of this...

Homework Statement Consider the following curve. y = 4 + 4x2 - 2x3. (a) Find the slope of the tangent to the curve at the point where x = a. Homework Equations m=y(a+h) - y(a)/h The Attempt at a Solution 1. m=y(a+h) - y(a)/h = -a^3-a^2+3ah+h^2-4 2. 6a^2 3. -6a^2+8a I know the derivative is...