SOLUTION: By a chord of the curve y = x3 we mean any line joining two distinct points on it. The number of chords which have slope 1 is (A) infinite (B) 0 (C) 1 (D) 2

Algebra ->  Trigonometry-basics -> SOLUTION: By a chord of the curve y = x3 we mean any line joining two distinct points on it. The number of chords which have slope 1 is (A) infinite (B) 0 (C) 1 (D) 2       Log On


   

Question 815301: By a chord of the curve y = x3 we mean any line joining two distinct points on it. The number of chords which
have slope 1 is
(A) infinite (B) 0 (C) 1 (D) 2
Answer by Edwin McCravy(20067) About Me  (Show Source):
You can put this solution on YOUR website!
A chord of slope 1 goes up at a 45° angle, and the curve
y = x³ is very much steeper than that in most places.
So it might be tempting to say there are only these two.
from the origin to (1,1) and from the origin to (-1,-1).
But don't be too hasty.....



....look again:



and I think you might consider that there are infinitely many other ones!

Edwin