Question

For function f(x)=2+4x^2 find and simplify the difference quotient:f(x+h)-f(x)_______ h

Answer 1

You have the following function:

`f(x)=2+4x^2`

and it is necessary to simplify the expression:

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

Proceed as follow:

`\begin{gathered} ((2+4(x+h)^2)-(2+4x^2))/(h)= \\ (2+4(x^2+2xh+h^2)-2-4x^2)/(h)= \\ (2+4x^2+8xh+4h^2-2-4x^2)/(h)= \\ (8xh+4h^2)/(h)=(8xh)/(h)+(4h^2)/(h)=8x+4h \end{gathered}`

Hence, the simplied expression is 8x + 4h