Part II: The Answers
266
Answers
401–500
404.
y
e x
e
=
−
7
4
3
4
4
You can begin by finding the y value, because it isn’t given:
f
e
e
( )
2
2
2
2
4
2
=
=
Next, find the derivative of the function:
(
)
x e
x
e
x
x
x
( )
( )
=
−
2
2
2
1
2
( )
x
f '
Substitute in the given x value to find the slope of the tangent line:
(
)
( )
e
e
e
( )
( )
( ( ))
( )
( )
2
2
22
1
2
7
4
2
2
2
4
2
2
=
−
=
f '
Now use the point-slope formula for a line to get the tangent line at x = 2:
y e
e x
y
e x
e
−
=
−
=
−
4
4
4
4
2
7
4
2
7
4
3
(
)
405.
y
x
= −
+
1
19
535
19
The normal line is perpendicular to the tangent line. Begin by finding the derivative
of the function f
 
(x) = 3x
2
+ x – 2:
x
=
+
6 1
( )
x
f '
Then substitute in the given x value to find the slope of the tangent line:
( )
( )
3 6 3 1 19
=
+ =
f '