Question

Please help. I would really appreciate it.

Answer 1

`f(x) = 3 {x}^(2) + 5x + 1 \\ \\ (f(x + h) - f(x))/(h) \\ \\ \frac{(3(x + h)^(2) + 5(x + h) + 1) - (3 {x}^(2) + 5x + 1 }{h} \\ \\ \frac{(3( {x}^(2) + 2xh + {h}^(2)) + 5x + 5h + 1) - 3 {x}^(2) - 5x - 1}{h} \\ \\ \frac{3 {x}^(2) + 6xh + 3 {h}^(2) + 5x + 5h + 1 - 3 {x}^(2) - 5x - 1 }{h} \\ \\ \frac{6xh + 3 {h}^(2) + 5h}{h} \\ \\ (h(6x + 3h + 5))/(h) \\ \\ = 6x + 3h + 5`