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.

$\frac{4(x+h)^2+3-(4x^2+3)}{h}$

solve the expression.

$\frac{4(x^2+2xh+h^2)+3-4x^2-3}{h}=\frac{4x^2+8xh+4h^2+3-4x^2-3}{h}$

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

$\frac{8xh}{h}=8x$

So the answer is 8x.