Is $f (x) = - 3 x^{5} - 2 x^{4} - 9 x^{2} + x - 7$ $f(x)=-3x^5-2x^4-9x^2+x-7$ concave or convex at $x = 5$ $x=5$ ?

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Answer 1 · 2017-12-18T00:16:20

$f’’(5) = -8118$ Less than zero, therefore concave.

$f’’(x) < 0$ at $x = 5$ (concave)
$f’’(x) > 0$ at $x = 5$ (convex)

$f’(x)=-15x^4-8x^3-18x+1$
$f’’(x)=-60x^3-24x^2-18$

$f’’(5)=-60(125)-24(25)-18 = -8118$ Less than zero, therefore concave.

Is f(x)=-3x^5-2x^4-9x^2+x-7f(x)=−3x5−2x4−9x2+x−7f(x)=-3x^5-2x^4-9x^2+x-7 concave or convex at x=5x=5x=5?