Consider the function

f(x) =x²+5x4.

Find the average rate of change of the function fromx₁tox₂.

(a)x₁= 1,x₂= 2

(b)x₁= 1,x₂= 1.5

(c)x₁= 1,x₂= 1.25

(d)x₁= 1,x₂= 1.125

(e)x₁= 1,x₂= 1.0625

(f)Does the average rate of change seem to be approaching one value? If so, state the value. (If not, enter DNE.) (g)Find the equations of the secant lines through the points (x₁,f(x₁)) and (x₂,f(x₂)) for parts(a)-(e).

part (a)

part (b)

part (c)

part (d)

part (e)

(h)Find the equation of the line through the point (1,f(1)) using your answer from part (f) as the slope of the line. (If your answer frompart (f)is DNE, enter DNE.)