Continuity and DifferentiabilityHard
Question
If y2 = p(x) is a polynomial of degree 3, then 
equals
equalsOptions
A.p′′′(x) + p′(x)
B.p′′(x) . p′′′(x)
C.p′(x) p′′′(x)
D.a contstant
Solution
Since, y2 = p(x)
On differentiating both sides, we get
2yy = P′(x)
Again, differentiating both sides, we get
2yy2 + 2y12 = p′′(x)
⇒ 2y3y2 + 2y2y12 = y2 p′′(x)
⇒ 2y3y2 = y2 p′′(x) - 2(yy1)2
⇒ 2y3y2 = p(x).p′′(x)
Again, differentiating, we get
(y3y2) = p′(x).p′′(x) + p(x) . p′′′(x)
⇒ (y3y2) = p(x). p′′(x)
⇒
= p(x). p′′(x)
On differentiating both sides, we get
2yy = P′(x)
Again, differentiating both sides, we get
2yy2 + 2y12 = p′′(x)
⇒ 2y3y2 + 2y2y12 = y2 p′′(x)
⇒ 2y3y2 = y2 p′′(x) - 2(yy1)2
⇒ 2y3y2 = p(x).p′′(x)
Again, differentiating, we get
(y3y2) = p′(x).p′′(x) + p(x) . p′′′(x) ⇒
(y3y2) = p(x). p′′(x)⇒
= p(x). p′′(x)Create a free account to view solution
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