Question

Let () = 5^2 − 9 + 11A. [4 pts] Find(+ℎ)−() /hand simplify your answer completely

Answer 1

`10x+5h-9`

Step-by-step explanation

given

`f(x)=5x^2-9x+11`

find

`(f(x+h)-f(x))/(h)`

Step 1

a)evaluate the function for (x+h)

so

`\begin{gathered} f(x)=5x^2-9x+11 \\ f(x+h)=5(x+h)^2-9(x+h)+11 \\ expand \\ f(x+h)=5(x^2+2xh+h^2)-9x-9h+11 \\ appply\text{ distributive property} \\ f(x+h)=5x^2+10xh+5h^2-9x-9h+11 \\ f(x+h)=5x^(2)+10xh+5h^(2)-9x-9h+11 \end{gathered}`

b) now replace

`\begin{gathered} (f(x+h)-f(x))/(h) \\ (5x^2+10xh+5h^2-9x-9h+11-(5x^2-9x+11))/(h) \\ (5x^2+10xh+5h^2-9x-9h+11-5x^2+9x-11)/(h) \\ add\text{ like terms in the numerator} \\ (10xh+5h^2-9h)/(h) \\ factorize\text{ h in the numerator} \\ (h(10x+5h^-9))/(h) \\ 10x+5h-9 \end{gathered}`

therefore,rthe answer is

`10x+5h-9`

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