How do i figure out a problem

Question

Calculate the average rate of change got f(x)=2x^2 +3 over the interval [2,2+h]

Answer 1

instantaneous rate of change = 4x = 4(2) = 8 when h approaches zero

which approximately = average rate of change for "small" h

average rate of change for h>0 is

[f(x+h)-f(x)]/(2+h-2)

= (2(x+h)^2 +3 - 2x^2 -3)/h

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

= (4xh+2h^2)/h

= 4x +2h

=4(2) + 2h

= 8 + 2h

2x^2 +3 is an upward opening parabola

slope of tangent line at x=2 is 8

for 2+h where h>0, the slope increases