Final answer:
The average rate of change from 1 to 6 is 7.8. An equation of the secant line containing (1, f(1)) and (6, f(6)) is y = 7.8x - 3.8.
Step-by-step explanation:
To find the average rate of change from 1 to 6, we need to find the change in the function values over that interval and divide by the change in x.
(a) Average rate of change = (f(6) - f(1))/(6 - 1) = (7(6) - 3) - (7(1) - 3)/(6 - 1) = (42 - 3) - (7 - 3)/5 = 39 - 4/5=38.2
(b) To find the equation of the secant line, we can use the point-slope form y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. The slope can be calculated as (f(6) - f(1))/(6 - 1) = 7.8. We can use the point (1, f(1)) = (1, 4) to find the equation: y - 4 = 7.8(x - 1), which simplifies to y = 7.8x - 3.8.