Consider the functionf(x)=2x

f(x)=2x312x272x+1on the interval[5,7]

[5,7].

The average or mean slope of the function on this interval is equal to

By the Mean Value Theorem, we know there exists ac

cin the open interval(5,7)

(5,7)such thatf

(c)

f(c)is equal to this mean slope. For this problem, there are two values ofc

cthat work:

The smaller onec

1

=

c1=

The larger onec

2

=

c2=