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Khaleesi Herbert

Answered question

2021-02-02

Find a second-degree polynomial P such that $P (4) = 5$ , $P^{'} (4) = 3$ , and $P^{″} (4) = 3$

Answer & Explanation

cheekabooy

Skilled2021-02-03Added 83 answers

Consider second degree polynomial $P (x) = a + b x + c x^{2}$ such that
$P (4) = 5, P' (4) = 3$ , and $P'' (4) = 3.$
$P (4) = 5 P (4) = 5$ gives us
$a + 4 b + 16 c = 5$ .
Now differentiating P, we get $P' = b + 2 c x$ . Now putting $x = 4$ , we get
$b + 8 c = 3$ .
Now differentiating P′, we get $P = 2 c P$ . Now putting $x = 4,$ we get
$b + 12 = 3 \Rightarrow b = - 9.$
Now putting $c = \frac{3}{2}$ and $b = - 9 i n e q 1$ we get

$a - 36 + 48 = 5 \Rightarrow a = - 7.$

So required second degree polynomial is $P (x) = - 7 - 9 x + (\frac{3}{2}) x 2$

Jeffrey Jordon

Expert2021-10-12Added 2605 answers

Answer is given below (on video)

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