Is $f (x) = - x^{5} + 3 x^{4} - 9 x^{3} - 2 x^{2} - 6 x$ $f(x)=-x^5+3x^4-9x^3-2x^2-6x$ concave or convex at $x = - 3$ $x=-3$ ?

Question

1551 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-04T15:59:50

*Answer could only be described as concave UPWARDS or DOWNWARDS (in your case, I'm not sure on how you view convex)

Answer: f''(-3) = 1022, hence, concave UPWARD

Method used: Second derivative test

Take the second derivative of f(x).
$f''(x)=-20x^3+36x^2-54x-4$

Then evaluate f(x) at x = -3

Is f(x)=-x^5+3x^4-9x^3-2x^2-6xf(x)=−x5+3x4−9x3−2x2−6xf(x)=-x^5+3x^4-9x^3-2x^2-6x concave or convex at x=-3x=−3x=-3?