Is $f(x)=-x^5-5x^3-3x^2+12x+8$ concave or convex at $x=-3$ ?

Question

1557 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-06T11:04:01

The curve is convex at $x=-3$

We calculate the first and second derivative

$f(x)=-x^5-5x^3-3x^2+12x+8$

$f'(x)=-5x^4-15x^2-6x+12$

$f''(x)=-20x^3-30x-6$

And

$f(-3)=-20*(-3)^3-30*(-3)-6$

$=-20*(-27)+90-6$

$=624$

Therefore,

As $f''(-3)>0$ , the curve is convex at $x=-3$

Is f(x)=-x^5-5x^3-3x^2+12x+8f(x)=-x^5-5x^3-3x^2+12x+8 concave or convex at x=-3x=-3?