Explicație pas cu pas:
[tex]f(x) = \frac{ {x}^{4} }{2} - 2 {x}^{3} + 3 \\[/tex]
[tex]f^{\prime}(x) = (\frac{ {x}^{4} }{2})^{\prime} - (2 {x}^{3})^{\prime} + (3)^{\prime} \\ = \frac{1}{2}( {x}^{4} )^{\prime} - 2( {x}^{3} )^{\prime} + 0 = \frac{1}{2} \times 4 {x}^{3} - 2 \times 3 {x}^{2} \\ = 2{x}^{3} - 6 {x}^{2} = 2 {x}^{2}(x - 3) [/tex]
