Question

Calculate and simplify the difference quotientg(x+h)-g(x)---------------- h

Answer 1

the expression is g(x)= 4x^2+3

g(x+h) = 4(x+h)^2+3

substitute the values in the given formula.

`(4(x+h)^2+3-(4x^2+3))/(h)`

solve the expression.

`(4(x^2+2xh+h^2)+3-4x^2-3)/(h)=(4x^2+8xh+4h^2+3-4x^2-3)/(h)`

The term 4h^2 is too small. so we can neglect it.

`(8xh)/(h)=8x`

So the answer is 8x.