FindA, B and C so that the lineAx+By=Cis tangent to the graph of f(x) =exand passes through (0,0).

Answer 1

m_tangent = f^'(x) = e^x and any point on the curve f(x) has coordinates (x , e^x). So a line thru a point on the curve and the origin has a slope = e^x/x and if we want that to = e^x then x = 1. So the point on the curve is (1 , e) and the tangent line has slope = e there. In pt-slope form this is y - e = e(x - 1). In general form this becomes ...

ex - y = 0. A = e , B = -1 , C = 0