Consider the linear function defined on the interval

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the linear function

q(x)=mx+5

defined on the interval

[0,t]

, where

t

is an integer such that

4\le t\le 8

and

m

is a real number. The average value of

q

on this interval is

7

. (i) Obtain the relation connecting

m

and

t

that results from the given average value. (ii) Using the additional restriction that

t

is an integer in the range

4\le t\le 8

, determine the corresponding integer value of

t

and the real value of

m