Hi Ahm97sic,
I saw your post on the Miscellaneous Ex. 19 Question 5a. about the integration of rate of change of bateria. Thanks, really help me a lot. I need another help from PAN A.M Textbook, Miscellanous 16, Page 15 (should be Page 364) , Question 15. Thanks
Regards,
Yaocatez
Dear Yaocatez,
Sorry for the late reply as I have not been visiting the sgforum AddMaths forum regularly.
Regards,
ahm97sic
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Question
If alpha is a positive root of the equation 2x^2 +px+18 = 0, calculate the value of alpha for which p has a stationery value and determine whether this value of p is a maximum or minimum.
Solution
(1) Since alpha (difficult to type alpha here, let alpha be a) is a positive root
ie x=a, substitue it into the equation we will get 2a^2 + pa +18 = 0.
(2) 2a^2 + pa +18 = 0
pa = - 2a^2 - 18
p = - 2a - 18/a
(3) dp/da = - 2 + 18/a^2
For stationary value, dp/da = 0
- 2 + 18/a^2 = 0
- 2a^2 + 18 = 0
a = 3 (a = - 3 is rejected as a is a positive root)
(4) dp/da = - 2 + 18/a^2
d^2p/da^2 = - 36/a^3
Substitute a= 3,
d^2p/da^2 = - 36/a^3 = - 36/27 = - ve ie p will be a maximum
Thank you for your kind attention.
Regards,
ahm97sic