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Find the coordinate of all points in the graph of y=3e^x - x^3 at which the tangent line passes through the point (1,0).

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I am told that the 2 points are (-.872, -1.027) and (2.275, 13.657). Any help at all that you can give will be very much appreciated.

I was thinking of letting the 2 coordinates be (X1, Y1) and (X2, Y2), calculating the slope of the line through (1,0) and one of these points, and setting this slope equal to the derivative of y=3e^x - x^3 ......but I seem to be going no where.

Suggestions?

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# Coordinates at which 2 tangent lines of a function pass through a single point

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