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Engineering Mathematics: Maxima and Minima - Dept. Of Applied Science

This presentation is on engineering mathematics maxima and minima, and is presented by Professor Rupali Yeole from the Department of Applied Science and Engineering of Hope Foundation’s International Institute of Information Technology. The presentation explains Maxima and Minima of functions of two independent variables, Stationary point and Extreme Value and explains how to determine the maxima and minima (extreme values) of a function.

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Engineering Mathematics: Maxima and Minima - Dept. Of Applied Science

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  1. https://www.quora.com/What-is-the-difference-between-local-minima-maxima-and-absolute-minima-maximahttps://www.quora.com/What-is-the-difference-between-local-minima-maxima-and-absolute-minima-maxima Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  2. Engineering Mathematics-I Maxima and Minima Prepared by : Prof. RupaliYeole Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  3. Maxima and Minima of Functions of Two Independent Variables • Let be a function of two independent variables and , which is continuous for all values of and in the neighborhood of i.e. be a point in its neighborhood which lies inside the region . Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  4. The point is called a point of relative minimum, if for all Then is called the relative minimum value. • The point is called a point of relative maximum, if for all Then is called the relative minimum value. Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  5. Stationary point: The point at which function is either maximum or minimum is known as stationary point. • Extreme Value: The value of the function at stationary point is known as extreme value of the function . Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  6. Working Rule To determine the maxima and minima (extreme values) of a function • Step I : Solve simultaneously for & • Step II: Obtain the values of Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  7. Step III: • If & at , then is maximum at & maximum value of the function is . • If & at , then is maximum at & maximum value of the function is . • If at , then is neither maximum nor minimum at .Such point is called Saddle Point. • If at , then no conclusion can be made about the extreme values of & further investigation is required. Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  8. Example 1 Q.1 Discuss the maxima and Minima of the function Answer: Let Step I: For extreme values Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  9. Therefore stationary point is . • Step II: Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  10. Step III: At Hence is maximum at Hope Foundation’s International Institute of Information Technology, I²IT, P-14 Rajiv Gandhi Infotech Park, Hinjawadi, Pune - 411 057 Tel - +91 20 22933441 / 2 / 3 | Website - www.isquareit.edu.in ; Email - info@isquareit.edu.in

  11. THANK YOU For further details please contact RUPALI YEOLE Department of Applied Sciences & Engineering Hope Foundation’s International Institute of Information Technology, I²IT P-14, Rajiv Gandhi Infotech Park, MIDC Phase 1, Hinjawadi, Pune – 411 057 www.isquareit.edu.in Phone : +91 20 22933441 / 2 / 3 rupaliy@isquareit.edu.in | info@isquareit.edu.in

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