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