[tex]f(a) = - 2 + 4 {a}^{2} [/tex]
[tex]f(a + h) = - 2 + 4 {(a + h)}^{2} = - 2 + 4 {a}^{2} + 8ah + 4 {h}^{2} [/tex]
[tex] \frac{f(a + h) - f(a)}{h} = 8a - 4h[/tex]
Step-by-step explanation:
[tex]f(a) = - 2 + 4 {a}^{2} [/tex]
[tex]f(a + h) = - 2 + 4 {(a + h)}^{2} = - 2 + 4( {a}^{2} + 2ah + {h}^{2} ) = - 2 + 4 {a}^{2} + 8ah + 4 {h}^{2} \\ [/tex]
[tex] \frac{f(a + h) - f(a)}{h} = \frac{- 2 + 4 {a}^{2} + 2 - 4 {a}^{2} + 8ah - 4 {h}^{2}}{h} = 8a - 4h[/tex]
