Question

Find all points on the graph of y=x^3-3x where the tangent line to the graph is parallel to the line y=24x+15?

Are the x-values for the answer 3 and -3? or is it just 3? Thanks.

Answer 1

(3,18) and (-3,-18)

Explanation:

You are right.

Slope of the graph at any point is `dy/dx = 3x^2 -3`. If the tangent line at some point, is parallel to y= 24x +15, then at that particular point, slope would be `3x^2-3 = 24` On solving this, `x = +- 3`

Thus there are two such points with x-coordinate `=+-3`. The points would be (i)`x=3, y=3^3 -3*3=18`, that is (3,18) and (ii)`x= -3, y= (-3)^3 -3(-3) = -18` that is (-3,18)