Find the average rate of change of f(x) = x^2 - 5x +2 from x=2 to x=5. Simplify your answer as much as possible.

Question

mathmate · Answer

Function = f(x)
Rate of change = f'(x)
average rate of change from x1 to x2=(f'(x2)-f'(x1))/(x2-x1)

If you need help finding f'(x), please post.

kity_kisses1234 · Answer

I need help finding f(x) sorry im not the best at math @mathmate

mathmate · Answer

f(x) is already given as:
f(x) = x^2 - 5x +2
you need to find the rate of change, which is f'(x) or dy/dx as is usually called in calculus.
Do you know how to find the derivative of a variable raised to a power?

mathstudent55 · Answer

@mathmate The derivative will give you the instantaneous rate of change at any x value.

The average rate of change between points $x_1$ and $x_2$ for a function is given by the rate of change formula:

${average~rate~of~change = \dfrac{change~ in~ f(x)}{change~in~x}} = \dfrac{f(x_2) - f(x_1)}{x_2 - x_1} $

mathmate · Answer

@mathstudent55 
Oh, what did I do!  You're right!  Probably did that before my morning coffee!
@kity_kisses1234 go with what @mathstudent55 posted. Sorry, I complicated things!

whpalmer4 · Answer

An intuitive way of looking at it: the average rate of change is just the difference between the ending point and the starting point, divided by the distance between them.

So, to find the average rate of change of your function $f(x) = x^2-5x+2$ when $x$ goes from $2$ to $5$, you figure out the value of $f(5)$, subtract the value of $f(2)$.  That gives you the change in the value of the function, and then you divide by $5-2$ which gives you the average rate of change.

If you have $10 today, and $50 2 days from now, your average rate of change of your cash on hand is (50-10)/2 = 20 dollars per day, right?  After one day, you have 10+20 = 30, and after two days, you have 10+20+20 = 5.  

Note that what happens in between the two end points DOES NOT MATTER.  Same average rate of change for both of these:

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