Step-by-step explanation:
[tex]f(x) = 3 {x}^{2} + 2x + 4[/tex]
[tex] \: [/tex]
[tex]f(2) = 3. {2}^{2} + 2.2 + 4[/tex]
[tex]f(2) = 3.4 + 4 + 4[/tex]
[tex]f(2) = 12 + 8[/tex]
[tex]f(2) = 20 \\ [/tex]
[tex] \: [/tex]
[tex]f(a + h) = 3 {(a + h)}^{2} + 2.(a + h) + 4[/tex]
[tex]f(a + h) = 3( {a}^{2} + 2ah + {h}^{2} ) + 2a + 2h[/tex]
[tex]f(a + h) = 3 {a}^{2} + 6ah + 3 {h}^{2} + 2a + 2h + 4[/tex]
[tex]f(a + h) = 3 {a}^{2} + 3 {h}^{2} + 6ah + 2a + 2h + 4[/tex]
