An application of derivative is shown here. To get the maximum volume of a box in same cost derivative helps us.

3. f(x) = x
2
f ‘(x) =
𝑑
𝑑𝑥
f(x) = 2x

8. Let, we've taken a 60*60 paper Then, measure what do the volume can be…….
x
60 – 2x
60 – 2x
x
This is the
time we
need

9. Derivative
helps us to
find the
maximum
Volume ……
60 cm
30cm
30cm
30 cm 30 cm
So, x = 10 cm

10. 10 cm
10 cm
(60 – 2*10)cm = 40 cm
Now,
The maximum volume = ( 10 * 40 * 40 ) cm3
= 16000 cm3
Let‘s justify the answer
𝑑2
𝑣
𝑑𝑥2
= −480 + 24𝑥
𝑑2
𝑣
𝑑𝑥2
𝑥=10
= −480 + 24(10)
𝑑2
𝑣
𝑑𝑥2
𝑥=10
= −240 < 0
Therefore producing the maximum

11. ‫الحاف‬ ‫هللا‬‫ظ‬
