Find-the-smallest-value-of-a-given-expression-x-2-6x-8-2-5-

Question Number 150119 by mathdanisur last updated on 09/Aug/21

Find the smallest value of a given

expression :

{(x^{2} + 6 x + 8)}^{2} + 5

Answered by Ar Brandon last updated on 09/Aug/21

f (x) = {(x^{2} + 6 x + 8)}^{2} + 5

f^{'} (x) = 2 (2 x + 6) (x^{2} + 6 x + 8) = 0

\Rightarrow x = - 3, x = - 2, x = - 4

f^{″} (x) = 2 (2 x + 6) (2 x + 6) + 4 (4 x^{2} + 6 x + 8)

f^{″} (- 4) > 0 \Rightarrow f (- 4) is minimum value

f (- 4) = {(16 - 24 + 8)}^{2} + 5 = 5

Commented by mathdanisur last updated on 09/Aug/21

Thank You S er

Answered by ajfour last updated on 09/Aug/21

y = {{(x + 3)}^{2} - 1}^{2} + 5

y_{m i n} = 5

w h e n x = - 3 \pm 1 = - 2, - 4

Commented by mathdanisur last updated on 09/Aug/21

Thankyou Ser