Application Of Derivative In Real Life.

f(x) = x2

f ‘(x) = 𝑑

𝑑𝑥f(x) = 2x

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

Derivative helps us to find the maximum Volume ……

60 cm

30

cm

30

cm

30 cm 30 cm

So, x = 10 cm

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

𝑑2𝑣

𝑑𝑥2= −480 + 24𝑥

𝑑2𝑣

𝑑𝑥2 𝑥=10

= −480 + 24(10)

𝑑2𝑣

𝑑𝑥2 𝑥=10

= −240 < 0

Therefore producing the maximum.

ظهللا الحاف