Question

Find the difference quotientwhere h= 0, for the function below.hf(x) = 3x²-8Simplify your answer as much as possible.f(x + n) - f(x)0믐hХ2

Answer 1

Given the function:

`f(x)=3x^2-8`
`\begin{gathered} f(x+h)=3(x+h)^2-8 \\ f(x+h)=3(x^2+2xh+h^2)-8 \end{gathered}`

Thus,

`\begin{gathered} (f(x+h)-f(x))/(h) \\ \Rightarrow(3(x^2+2xh+h^2)-8-(3x^2-8))/(h) \end{gathered}`
`(3x^2+6xh+3h^2-8-3x^2+8)/(h)`
`(6xh+3h^2)/(h)`

Hence, the final answer is:

`\begin{gathered} (3h(2x+h))/(h) \\ \Rightarrow3(2x+h) \\ \end{gathered}`