Question

I need help asap solving this!​

Answer 1

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Explanation:

`f(x) = 4 - 6x + 3 {x}^(2)...(1) \\ plug \: x = a \: in \: (1) \\ f(a) = \boxed{ 4 - 6a + 3 {a}^(2) } \\ \\ next \: plug \: x = (a + h) \: in \: (1) \\ f(a + h) = 4 - 6(a + h) + 3 {(a + h)}^(2) \\ = 4 - 6a - 6h + 3( {a}^(2) + {h}^(2) + 2ah) \\ = 4 - 6a - 6h + 3 {a}^(2) + 3{h}^(2) + 6ah \\ f(a + h) = \boxed{3 {a}^(2) + 3{h}^(2) + 6ah - 6a - 6h + 4} \\ \\ now \\ \\ (f(a + h) - f(a))/(h) \\ \\ = \frac{(3 {a}^(2) + 3{h}^(2) + 6ah - 6a - 6h + 4) -(4 - 6a + 3 {a}^(2) ) }{h} \\ \\ = \frac{3 {a}^(2) + 3{h}^(2) + 6ah - 6a - 6h + 4 -4 + 6a - 3 {a}^(2) }{h} \\ \\ = \frac{ 3{h}^(2) + 6ah - 6h }{h} \\ \\ = \frac{3h( {h} + 2a - 2) }{h} \\ \\ (f(a + h) - f(a))/(h) = \boxed{ 3( 2a + h - 2)}`