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?

Question

solomonzelman · Answer

If this is a calculus problem, then:

$\large\color{black}{ \displaystyle f'(x)=3x^2  }$
$\large\color{black}{ \displaystyle 1=3x^2  }$
$\large\color{black}{ \displaystyle 1/3=x^2  }$

$\large\color{black}{ \displaystyle x=\pm\frac{\sqrt{3}}{3}  }$

solomonzelman · Answer

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.