Use the graph below for this question: graph of parabola going through 2, negative 3 and 3, negative 1. what is the average rate of change from x = 2 to x = 3? 2 305

The average rate of change of a function f(x) on the interval [a,b] is given by:

f(b) - f(a)

  b-a

In this specific case, a=2 and b = 3.

f(2) = -3 and f(3) = -1.

Thus, the average rate of change here of f(x) on the interval [2,3] is:

-1 - (- 3)             2

= = 2 (answer)

    3-2               1

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4