Question

calculate and simplify for the difference quotientg(x+h)-g(x)_________ hfor the function defined by g(x)=4x^2+3

Answer 1

g(x+h) means putting x+h into x of the function g(x)

So, lets simplify:

`\begin{gathered} (4(x+h)^2+3-\lbrack4x^2+3\rbrack)/(h) \\ =(4(x^2+2xh+h^2)+3-4x^2-3)/(h) \\ =(4x^2+8xh+4h^2+3-4x^2-3)/(h) \\ =(8xh+4h^2)/(h) \\ =(h(8x+4h))/(h) \\ =8x+4h \end{gathered}`