Hi there.
For g(x)=4x² -3x +1 Find the rate of change for:
A) x=1 and x=3
B) (x, f(x)) and (x+h, f(x+h)
I dont know how and would appreciate an explanation. Thanks so much.
Perhaps you just need the definition for average rate of change?
Between x=a and x=b, the average rate of change is (change in g(x) divided by the change in x):
$\displaystyle
\displaystyle \frac{g(b) - g(a)}{b - a}
$
For example, average rate of change between x=0 and x=1 is
$\displaystyle
\displaystyle \frac{g(1) - g(0)}{1 - 0} = \frac{(4(1)^2 -3(1) +1) - (4(0)^2 -3(0) +1)}{1 - 0} = 1
$
numerator again ...
$\displaystyle 4(x + h)^2 - 3(x + h) + 1 - (4x^2 - 3x + 1) =$
$\displaystyle 4(x^2 + 2xh + h^2) - 3(x + h) + 1 - (4x^2 - 3x + 1) =$
$\displaystyle 4x^2 + 8xh + 4h^2 - 3x - 3h + 1 - 4x^2 + 3x - 1 =$
$\displaystyle 8xh + 4h^2 - 3h =$
$\displaystyle h(8x + 4h - 3)$