Question

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.

Answer 1

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.