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August 22, 2014

August 22, 2014

Posted by **Samantha** on Wednesday, November 5, 2008 at 6:24am.

So I found the derivative which is 3x^2.

Let (a, a3) be the point of tangency.

3x^2 = (a3 - 1/4)/(a-0)

I'm not sure how to solve for a.

Yes, the point is (0,1/4) but it's not on the curve. It's on the tangent line. I'm not sure how to solve for a and a3 in that equation. My algebra is bad.

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How do you do this question.

f(x) = (5x-1)/(2-3x), find f^(-1)(x). The answer is supposed to be (1+2x)/(5+3x).

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And can you please explain this one to me.

Suppose that xy^(3)+2y^(2)+xy+2x^(3) = 0. Find the general expression for dy/dx. Also, find the value of dy/dx at the point where x = 1.

I have no idea how to differentiate that.

Thanks so much for the help!

- Calculus - Damon -
**Dr Russ**, Wednesday, November 5, 2008 at 8:40amI get

1) 3a^2=(a^3-1/4)/a

3a^3=a^3-1/4

2a^3= -1/4

a^3=-1/8

so a = -1/2

Thus the line has gradient

3(-1/2)^2 = 3/4

and equation

y=(3/4)x+1/4

or

4y=3x+1

- Calculus - Damon -
**Samantha**, Wednesday, November 5, 2008 at 12:17pmThanks so much!

- Calculus - Damon -

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