Find-concave-up-and-concove-down-of-function-f-x-x-2-x-3-

Question Number 121956 by bemath last updated on 13/Nov/20

F i n d c o n c a v e u p a n d c o n c o v e d o w n

o f f u n c t i o n f (x) = x^{2} ∣ x - 3 ∣

Answered by MJS_new last updated on 13/Nov/20

f (x) = {\begin{cases} 3 x^{2} - x^{3}; x < 3 \\ x^{3} - 3 x^{2}; x ⩾ 3 \end{cases}

f^{″} (x) = {\begin{cases} 6 - 6 x; x < 3 \\ 6 x - 6; x ⩾ 3 \end{cases}

\Rightarrow

f (x) is concave {\begin{cases} up; x < 1 \\ down; 1 < x < 3 \\ up; 3 < x \end{cases}

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