Posted by Anonymous on Monday, October 15, 2012 at 11:06am.
The curve crosses the y axis when x = 0.
f(0) = 3*e^0 - 3 = 0 @ x=0
dy/dx = 12 e^4x = 12 @ x=0
The straight tangent line at the origin (the tanglent point) is
y = 12 x.
y=0 when x=0, so we are looking at the line through (0,0)
f'(x) = 12e^4x
f'(0) = 12
the line is thus y=12x
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