f ( 0 ) = e^0 ( 5 cos 0 + 2 sin 0 = = 1 5 = 5
f ( x ) = - e^(-x) ( 5 cos x + 2 sin x ) + e^(-x) ( - 5 sin x + 2 cos x ) =
( using the chain rule )
= e^(-x) ( - 5 cos x - 2 sin x - 5 sin x + 2 cos x ) =
= e^(-x) ( - 3 cos x - 7 sin x )
f ( x ) = 1 ( - 3 - 0 ) = - 3
The equation of the tangent line:
y - f ( 0 ) = f ` ( 0 ) ( x - 0 )
y - 5 = - 3 x
y = - 3 x + 5
The x - intercept of the tangent line:
0 = - 3 x + 5
3 x = 5
x = 5 / 3
or ( 5/3, 0 )
