[tex]h(4) = -64[/tex]
Given:
[tex]h(x) = \frac{1}{2}x^4 -3x^3\\[/tex]
[tex]h(4) = \frac{1}{2}(4)^4 -3(4)^3 \\ h(4) = \frac{1}{2}(256) -3(64) \\ h(4) = 128 -192 \\ h(4) = -64[/tex]