Consider the functionf(x)=3x.
a. Determine an expression, in terms of a and h, for the average rate of change between the points (a,f(a)) and ( a + h, f(a+h) ) for the function . Show all steps needed to find a simplified algebraic expression.
b. Using your expression from (a), determine the average rate of change from x = -1 to x = 2. (no decimal values)
looks like you are asked to find the slope, using first principles, of a straight line y = 3x
you have the points (a, 3a) and (a+h, 3(a+h))
avg rate of change = (3(a+h) - 3a)/(a+h - a)
= (3a + 3h - 3a)/h
= 3h/h
= 3, if h ≠0
b) I got a constant, so it would be 3
You could repeat my process, let a = -1 and h = 2-(-1) = 3