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ilovealgebra

Member

Registered: 2006-10-02

Posts: 40

more differentiation

Hi, I dont know how many questions im allowed to ask on here, so just tell me enough is enough when i get too carried away

These types of questions are giving me alot of grief..

1. Show that any two tangent lines to the parabola y=ax², a≠0,intersect at a point that is on the vertical line halfway between the points of tangency

2. Suppose L is the tangent line at x=x0 to the graph of the cubic equation y=ax ³ +bx. Find the x-coordinate of the point where L intersects the graph a second time.

3.Show that the segment of the tangent line to the graph of y=1/x that is cut off by the coordinate axes is bisected by the point of tangency.

Thanks for the help

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"...nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question (much less condemned) upon the testimony of biblical passages."
-Galileo Galilei

Equation

Member

Registered: 2009-04-15

Posts: 1

Re: more differentiation

If 6+6 =72,    7+2=63,    6+5=66 Then 9+7=...........??

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: more differentiation

1.

so the two lines are:

finding the constants

sub x = x_0, y = ax^2

similarly

so the two lines are:

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2.

so L is

since L is a tangent, two of the solutions to this cubic must be x = x0, dividing by (x-x0)^2 we get

so L will intersect the graph a second time at x = -2x_0

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3.Show that the segment of the tangent line to the graph of y=1/x that is cut off by the coordinate axes is bisected by the point of tangency.

y = 0

so the tangent runs between x = 0, and x = 2x0, the midpoint of which is x = x_0, the tangency point

Last edited by luca-deltodesco (2009-04-16 00:53:22)

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: more differentiation

Wrong.

oops ^^, (fixed it)

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The Beginning Of All Things To End.
The End Of All Things To Come.