Write an equation in slope-intercept form for the line that satisfies the following condition.
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A generic point on the graph of the curve has coordinates
The derivative gives us the slope of the tangent line at a given point:
Let k be a generic x-coordinate. The tangent line to the curve at this point will pass through and have slope
So, we can write its equation using the point-slope formula: a line with slope m passing through has equation
In this case, and
, so the equation becomes
We can rewrite the equation as follows:
We know that this function must give 0 when evaluated at x=0:
This equation has no real solution, so the problem looks impossible.