Posted by **Joe** on Tuesday, October 4, 2011 at 10:56pm.

If f(x)=[(x−1)/(1+5x)], there are two points on the graph of

y=f(x) at which the tangent lines are parallel to the line x−2y=2.

Type in the x values of

these points. Type the smaller number first, then the larger number.

- Calculus -
**Steve**, Wednesday, October 5, 2011 at 4:55am
Sure, I'll type 'em in -- what are they?

Oh, you mean I have to solve for them first? OK, here goes.

The line x-2y=2 has slope 1/2

f(x) has slope 10/(5x+1)^2 for all x ≠ -1/5

SO, we have to find where the slope = 1/2

10/(5x+1)^2 = 1/2

20 = (5x+1)^2

20 = 25x^2 + 10x + 1

25x^2 + 10x - 19 = 0

x = -1.09 or 0.69

If you sketch the curve, you'll see that this appears correct.

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