Posted by sam on .
consider the function f(x)=x^2-6x+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) -
[ value of the function at 3 - value of the function at -1} / 4
f(x+h) = x^2 + 2 x h + h^2 - 6x-6h +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
what is 2x-6 when x = 3 ???
2x-6 = -4 when x = 1
If you are having trouble with this, you should read the chapter on the subject more carefully. It is fundamental.