# Finding a line passing through a known point/tangent to a curve at an unknown point

## Homework Statement

Find the line passing through the point (0,-18) and tangent to the curve y=x^3-2 at some point.

y=mx+b

## The Attempt at a Solution

Well, I know the derivative is 3x^2, and that should be the slope of the line at the point of tangency. I'm just not sure how to find out what point the curve shares with the line! I know that seems like a pretty bad attempt at a solution, I just need a hint about where to start with this one.

SammyS
Staff Emeritus
Homework Helper
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The line you want passes passes through a point on the curve y = x3 - 2 , so, as an ordered pair, this point is (x, x3 - 2). The slope of the line is given as
m = 3x2, for the same value of x that's in the ordered pair.

Now, we could use the point - slope form of a line, but the point given to us is the y intercept for any line passing through it. Use the slope-intercept form of a line. y = mx + b, where b = -18.

(x3 - 2) = (3x2)(x) - 18 .

Solve this equation for x, to find the x value for a point on the parabola.