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January 23rd, 2013, 02:06 PM
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I want to appear for Indian institute of technology JEE so can you provide me question paper with solution in PDF format. Here I am providing the solved question paper for IIT JEE. Q.Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and p(3) = 2, then p (0) is Ans:- [9] Since least degree hence p(x) is cubic. Let p (x) = ax3+ bx2+ cx + d p (1) = 6 = a + b + c + d …… (1) p (3) = 2 = 27a + 9b + 3c + d …… (2) p'(x) = 3ax2+ 2bx + cp'(1) = 0 = 3a + 2b + c …… (3) p’(3) = 0 = 27a + 6b + c …… (4) (4) (3) 24a + 4b = 0 b = 6a …… (5) (2) (1) 4 = 26a + 8b + 2c From (5) -4 = 26a 48a + 2c 4 22a c 11a 2 2 …… (6) From (3) 3a + 2b + c = 0 3 (a) + 2 ( 6a) + (11a 2) = 0 3a - 12a + 11a 2 = 0 2a = 2 a = 1 c = f (0) = 11a 2 = 11 - 2 = 9 For the complete solved question paper click on the attachment. Last edited by Anuj Bhola; October 17th, 2019 at 12:25 PM. |
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