f-x-x-2-1-x-3-Find-f-1-

Question Number 108901 by ZiYangLee last updated on 20/Aug/20

f (x) = x^{2} {(1 + x)}^{3}

Find f^{″} (1) .

Answered by malwaan last updated on 20/Aug/20

f^{'} (x) = x^{2} \times 3 {(1 + x)}^{2} + {(1 + x)}^{3} \times 2 x

= {(1 + x)}^{2} (3 x^{2} + 2 x + 2 x^{2})

= {(1 + x)}^{2} (5 x^{2} + 2 x)

\Rightarrow f^{″} (x) = {(1 + x)}^{2} (10 x + 2) +

(5 x^{2} + 2 x) (2) (1 + x)

∴ f^{″} (1) = 4 \times 12 + 7 \times 2 \times 2

= 48 + 28 = 76

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