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

Answer 1

f(x) = e^x

f'(x) = e^x = slope of the graph = m where y=mx

mx = e^x

x=1

m(1) = e^1 = e

m=e = about 2.7

the point of the line tangent to f(x) e^x is (1,e) or about (1,2.7)

the line is y=ex where the standard equation y=mx has m=e= about 2.7

Ax+By= C = 0, By=-Ax, or y = (-A/B)x where m=-A/B

because it goes through the origin, it's of the form y=mx where m=-A/B = e

-A/B = 2.7/1 = e/1

B=1, A=-e

-ex + y = 0

y= f(x) = ex

line through the origin with same slope is y=(e^x)x = xe^x