Question

by a chord of the curve y=x^3 we mean any line joining two distinct points on it.the number of chords which have slope 1 will be?

Answer 1

If this is a calculus problem, then:

\(\large\color{black}{ \displaystyle f'(x)=3x^2 }\)
\(\large\color{black}{ \displaystyle 1=3x^2 }\)
\(\large\color{black}{ \displaystyle 1/3=x^2 }\)

\(\large\color{black}{ \displaystyle x=\pm\frac{\sqrt{3}}{3} }\)

Answer 2

We obtain the slope by taking the derivative of the function, and then set the derivative (or the slope) equal to 1. After doing so we obtained the following answers.