Question

Question #58e63

Answer 1

`g(x)=210+8x^3+x^4`

`g'(x)=24x^2+4x^3`

`g''(x)=48x+12x^2=12x(4+x)=0 => x=0,-4`

Since `g''`changes its sign at `x=-4,0`, there are inflection points there.

`g(-4)=210+8(-4)^3+(-4)^4=-46`

`g(0)=210+8(0)^3+(0)^4=210`

Hence, its inflection points are `(-4,-46)` and `(0,210)`.

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I hope that this was helpful.