Question

For the function f(x)=x^3-4x^2+x+3, find the average rate of change from x=1 to x=3.

Can someone please explain this problem step by step I keep messing it up.

Medal!

Answer 1

Average rate of change from x=1 to x=3 is: { f(3) - f(1) } / { 3 - 1} = { f(3) - f(1) } / 2
f(x)=x^3-4x^2+x+3
f(3) = ?
f(1) = ?
Plug the numbers into the average formula.

Answer 2

I got -2 but I don't think thats right?

Answer 3

For a simple linear function, for example, y = 5x + 3, you know your slope is 5. It's a line, the slope doesn't change. When you have a higher-order function (in this case, a 3rd degree polynomail), you typically have a curvy function (some functions have cusps, some have breaks, etc...). Anyway, by average, you are essentially just finding the slope of the straight line that connects those two points. First you find your y values from your given x-values. You plug in each x to find y.

When x_1 = 1, you plug that into your function to find y. That x_1,y_1 is your first point.

When x_2=3, you plug that into the function to find y_2. That x_2,y_2 is your 2nd point.

Not you just apply the point-slope formula: (y_2-y_1) / (x_2 - x_1) = m = slope = average rate of change

hope this helps

Answer 4

On this question the first time I tried it I got -7/3 and the 2nd time I got -2?

Answer 5

I too got -2.