Part II: The Answers
234
Answers
301–400
296.
f '(1) < f '(2) < 0.1 < f '(5)
The slope of the tangent line at x = 1 is negative, the slope of the tangent line at x = 2 is
equal to zero, and the slope of the tangent line at x = 5 is clearly larger than 0.1.
Therefore, f '(1) < f '(2) < 0.1 < f '(5).
297.
5
Use basic derivative rules to get f '(x) = 5.
298.
2x + 3
Apply the power rule to each term, recalling that the derivative of a constant is zero:
f '(x) = 2x + 3.
299.
4x + 7
Begin by multiplying the two factors together:
f x
x
x
x
x
( ) =
+
(
) −
(
)
=
+ −
4 2 1
2
7
4
2
Then apply the power rule to get the derivative:
f x
x
x
’( ) = ( )+
=
+
2 2
7
4
7
300.
0
Because π
3
is constant, f '(x) = 0.
301.
5
2 x
Split up the radical and rewrite the power on the variable using exponential notation:
f x
x
x
x
( ) =
=
=
5
5
5
1 2
Then apply the power rule to find the derivative:
f x
x
x
x
’( ) = ( ) = =
−
5 1
2
5
2
5
2
1 2
1 2
302.
− −
+
3
2
12
2
3
4
x
x
x
Begin by breaking up the fraction:
f x
x
x
x
x
x
x
x
x
x
x
x
( ) =
+ −
=
+
−
=
+
−
−
−
−
3
4
3
4
3
4
2
3
2
3
3
3
1
2
3