Answers and Explanations 279
Answers
401–500
426.
L(x) = 6x – 3
Finding the linearization L(x) is the same as finding the equation of the tangent line.
First find a point on the line by entering the value of a in the function. For the given
value of a, the corresponding y value is
f 1 3 1
3
2
( ) ( )
=
=
Next, find the derivative of the function to get the slope of the line:
′
′
f x
x
f
( )
( )
( )
=
=
=
6
1 6 1 6
Using the point-slope formula with the slope m = 6 and the point (1, 3) gives you
y y m x x
y
x
y
x
y
x
− =
−
− =
−
=
− +
=
−
1
1
3 6
1
6
6 3
6
3
(
)
(
)
Replace y with L(x) to get the solution: L(x) = 6x – 3.
427.
L x
x
( ) = − + +
π 2
2
Finding the linearization L(x) is the same as finding the equation of the tangent line.
First find a point on the line by entering the value of a in the function. For the given
value of a, the corresponding y value is
f π
π
π
2
2
2
1
( ) = + =
cos
sin