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

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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#