A function is given. f(x) = 4 − 3x2; x = 5, x = 5 + h

Question

Determine the net change between the given values of the variable

 Determine the average rate of change between the given values of the variable. 

Answer 1

The net change is just looking for the difference between f(5) and f(5+h). So you want to evaluate the function at x=5 and x=5+h and then calculate f(5+h)-f(5). Your answer will still have the variable h in it.

The rate of change is looking for the change in the function f(x) per unit change in x. In formal notation this looks like (f(x2)-f(x1))/(x2-x1). It's basically looking for the slope of a line connecting two points on the curve. So for this question you will take the answer from the first part and divide by the difference between the two x values (x+h)-x.

I hope that helps you figure it out.

Answer 2

f(x) = 4 - 3x²

f(5) = 4 - 3(5)²= 4 - 75 = -71

f(5+h) = 4 - 3(5+h)² = 4 - 3(5+h)(5+h) = 4 - 3(5*5 + 5h + 5h + h*h) = 4 - 3(h²+10h +25) = 4 - (3h²+30h +75)

= -3h² - 30h - 71

f(5+h) - f(5) = -3h² - 30h - 71 - (-71) = -3h² - 30h

average rate of change = [f(5+h) - f(5)] / [(5+h) - (5)] = [f(5+h) - f(5)] / h = (-3h² - 30h)/h = (-3h²)/h - (30h)/h

= -3h - 30