Determine the equation of the tangent line at the indicated -coordinate.
f(x) = e^(-0.4x) * ln(18x) for x= 3
The equation of the tangent line in slope-intercept form is
when x = 3
f(3) = 1.201 , correct to 3 decimals
so the point of contact is (3, 1.201)
f ' (x) = e^(-.4x) (1/x) + (-.4) e^(-.4x) ln(18x)
f ' (3) = -.380 correct to 3 decimals
y - 1.201 = -.38(x-3)
y = -.38x + 2.342
better check my arithmetic and button-pushing