Answer:To find the original function
�
(
�
)
C(x), you integrate
�
�
�
�
dx
dC
with respect to
�
x:
�
(
�
)
=
∫
(
16
3
�
+
9
)
�
�
C(x)=∫(
3
16
x+9)dx
�
(
�
)
=
8
3
�
2
+
9
�
+
�
C(x)=
3
8
x
2
+9x+K
Now, to determine the constant of integration (
�
K), you can use the given information that
�
=
180
C=180 when
�
=
17
x=17:
180
=
8
3
(
17
)
2
+
9
(
17
)
+
�
180=
3
8
(17)
2
+9(17)+K
Solve for
�
K:
180
=
8
3
(
289
)
+
153
+
�
180=
3
8
(289)+153+K
180
=
2312
3
+
153
+
�
180=
3
2312
+153+K
180
=
770.
6
‾
+
153
+
�
180=770.
6
+153+K
180
≈
923.
6
‾
+
�
180≈923.
6
+K
�
≈
180
−
923.
6
‾
K≈180−923.
6
�
≈
−
743.
6
‾
K≈−743.
6
Now, you can write the complete expression for
�
(
�
)
C(x):
�
(
�
)
=
8
3
�
2
+
9
�
−
743.
6
‾
C(x)=
3
8
x
2
+9x−743.
6
Therefore, the function
�
(
�
)
C(x) is given by the equation above.
Explanation: