Find a point on the curve `y=x^3-3x` where the tangent is parallel to the chord joining `(1,-2)a n d(2,2)dot`

Explanation

Given curve `y=x^3-3x`
we have to Find a point on the curve where the tangent is parallel to the chord joining `(1,-2)a n d(2,2)`
As tangent is parallel to the chord passing through given points, Therefore there slopes will be equal.
Slope of chord,
`m=(2+2)/(2-1)`
`=4`
Differentiating the given equation, we get
`(dy)/(dx)=3x^2-3=4`
`=>x=sqrt(7)/sqrt(3) or x=-sqrt(7)/sqrt(3) `
On putting a value of x in the given equation, we get
`y= (2sqrt(7))/(3sqrt(3)) or y=-(2sqrt(7))/(3sqrt(3))`