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.

1 Answer
Dec 8, 2017

(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)