Posted by sam on .
consider the function f(x)=x^26x+12
a. find the average rate of change over the interval [1,3]
b. use the definition of the derivative to find f prime(x)
c. find the instantaneous rate of change at the point where x=3
d. find the value of x on the interval [1,3] such that f prime(x) = 4

calculus (rate of change) 
Damon,
a.
[ value of the function at 3  value of the function at 1} / 4
b.
f(x+h) = x^2 + 2 x h + h^2  6x6h +12
f(x) = x^2  6x + 12
f(x+h) f(x) = 2xh +h^2 6h
divide by h
2x + h  6
let h >0
2x  6
c.
what is 2x6 when x = 3 ???
d.
2x6 = 4 when x = 1
If you are having trouble with this, you should read the chapter on the subject more carefully. It is fundamental.