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`f(x) = (1/2)x^4 + 2x^3` Find the points of inflection and discuss the concavity of the graph of the function.

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Given: `f(x)=(1/2)x^4+2x^3`

Find the critical values for x by setting the second derivative of the function equal to zero and solving for the x value(s).

`f'(x)=2x^3+6x^2`

`f''(x)=6x^2+12x=0`

`6x(x+2)=0`

`x=0,x=-2`

The critical value for the second derivative is x=0 and x=-2. 

If f''(x)>0, the curve is...

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