Find the average rate of change of the function

Question

Find the average rate of change of the function f(x)=7/3x−6, on the interval x∈ [-4,0]. 

Answer 1

y = (7/3)x -6

rate of change from x=-4 to x=0

y' = 7/3 for the given interval or for any interval.

it's a straight line with a constant rate of change = the slope = a constant = 7/3

UNLESS

you meant

y = 7/(3x), a rectangular hyperbola with vertical asymptote x=0

then

y'(x) = [(7/3)x^-1]' = -(7/3)/x^2

y'(-4) = -(7/3)/16 = -7/48

y'(0) = -(7/3)/0^2 = Undefined = rate of change at x=0

average rate of change is also undefined

average rate of change would = slope of the secant line, but there is no secant line