Application Of Derivative In Real Life.
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The document discusses the process of finding the maximum volume of a box created from a 60 cm x 60 cm square paper by cutting out squares from the corners. Using calculus, it determines that cutting out squares of 10 cm results in a maximum volume of 16,000 cm³. The second derivative test confirms that this volume is indeed a maximum.
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Application Of Derivative In Real Life.
- 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