Hence, the length of the shadow increases at the rate 5
2 km/h Example 33 Find intervals in which the function given by
f (x) =
4
3
2
3
4
36
3
11
10
5
5
x
x
x
x
−
−
+
+
is (a) increasing (b) decreasing Solution We have
f (x) =
4
3
2
3
4
36
3
11
10
5
5
x
x
x
x
−
−
+
+
Therefore
f ′(x) =
3
2
3
4
36
(4
)
(3
)
3(2 )
10
5
5
x
x
x
−
−
+
= 6(
1)(
2)(
3)
5 x
x
x
−
+
−
(on simplification)
Fig 6 21
Rationalised 2023-24
 MATHEMATICS
180
Now f ′(x) = 0 gives x = 1, x = – 2, or x = 3