# Ex 6.5,6 - Chapter 6 Class 12 Application of Derivatives

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 6.5,6 Find the maximum profit that a company can make, if the profit function is given by ๐(๐ฅ) = 41 โ 72๐ฅ โ 18๐ฅ2 The profit function is given by p(x) = 41 โ 72x โ 18x2 pโ(x) = โ72 โ 36 x Putting pโ (x) = 0 โ72 โ 36x = 0 โ36x = 72 ๐ฅ =๏ทโ72๏ทฎ36๏ทฏ= โ2 Now, Pโ(x) = โ36 Since Pโ (x) < 0 ๐ฅ=โ2 is the maxima โด Maximum profit = p(โ2) p(x) = 41 โ 72x โ 18x2 ๐(โ2)=41โ72 ๏ทโ2๏ทฏโ18 ๏ท๏ทโ2๏ทฏ๏ทฎ2๏ทฏ =41+144โ18 ๏ท4๏ทฏ =41+144โ72 =113 Hence, the maximum profit is 113 unit.

Chapter 6 Class 12 Application of Derivatives

Concept wise

- Finding rate of change
- To show increasing/decreasing in whole domain
- To show increasing/decreasing in intervals
- Find intervals of increasing/decreasing
- Finding slope of tangent/normal
- Finding point when tangent is parallel/ perpendicular
- Finding equation of tangent/normal when point and curve is given
- Finding equation of tangent/normal when slope and curve are given
- Finding approximate value of numbers
- Finding approximate value of function
- Finding approximate value- Statement questions
- Finding minimum and maximum values from graph
- Local maxima and minima
- Minima/ maxima (statement questions) - Number questions
- Minima/ maxima (statement questions) - Geometry questions
- Absolute minima/maxima

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.