# Math Help - Implicit differentiation find points where slope is ___

1. ## Re: Implicit differentiation find points where slope is ___

I get $y = \pm 2\sqrt{10\sqrt{5}-22}$

That isn't correct?

What about the third point? $-2x(x^2-4x-16)=0$ has three solutions. $x=0$ is also a solution.

2. ## Re: Implicit differentiation find points where slope is ___

the diagram shows the curve not going past x = 4 because it goes into an asymptote (according to the diagram at least) and the problem stated to use the diagram.

the book gives the point (2 -2sqrt5, -2sqrt(10 sqrt(5) -22) but in solving for x, I did see that x = 0 was a solution but the book didn't have that as an answer. Inputing the value of x back into the original equation as 0, it yields y= 0. the point is then (0, 0)

4. ## Re: Implicit differentiation find points where slope is ___

If you plug (0,0) into the derivative you found, you are dividing by zero. So, that was my mistake. The derivative is not defined at (0,0), so the function does not have a tangent line at that point.

5. ## Re: Implicit differentiation find points where slope is ___

Originally Posted by Jonroberts74
the diagram shows the curve not going past x = 4 because it goes into an asymptote (according to the diagram at least) and the problem stated to use the diagram.

the book gives the point (2 -2sqrt5, -2sqrt(10 sqrt(5) -22)
This is the answer I got, as well. Maybe whatever answer you got is equal with a little algebra.

6. ## Re: Implicit differentiation find points where slope is ___

I got the same answer as you.

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