consider the function f(x)=x^2-6x+12

Question

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

Answer 1

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 - 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

c.
what is 2x-6 when x = 3 ???

d.
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.