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InterviewSolution
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P(x) be a polynomial of degree 3 satisfying P(-1) =10 , P(1) =-6 and p(x) has maxima at x = -1 and p(x) has minima at x=1 then The value of P(1) isA. -12B. -10C. 15D. 21 |
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Answer» Correct Answer - 1 P(x) is polynomial of degree 3 Given p(x) has minima at x=1 `therefore p(x) =a(x-1)` `therefore p(x)=a(x^(2)/(2)-x)+b` Given p(x) has maximum at x =-1 `therefore p(-1)=a(x^(2)/(2)-x)+b` Given p(x) has maxima at x =-1 `therefore b=-3/2a` `therefore p(x)=a(x^(3)/(6))-(x^(2)/(3)x)+C` Given p(-1)=10 `therefore a(-1/6-1/2+3/21)+C=10` `therefore 5a+6c=60` `therefore p(1)=a(1/6-1/2-3/2)+c=-6` solving (1) and (2) we get a=6 an c=5 `therefore p(x)=x^(3)-3x^(2)-9x+5` `therefore p(2)=8-12-18+5=-17` `p(x)=3x^(2)-6x-9` `therefore p(1)=3-6=-12` |
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