Question

Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001. (Technology is recommended for the cases h = 0.01, 0.001, and 0.0001.) HINT [See Example 4.] (Round your answers to five decimal places.) f(x) = 3 x ; a = 4

Answer 1

The average rate of change of the function f(x)over the interval [a,b] can be expressed as:

average rate of change=(f(b)?f(a)) ÷ (b-a)

So, for the function f(x)=3x and the interval [a,a+h], this becomes

(f(a+h) - f(a)) ÷ ((a+h) - a)

Put a = 4, we get

(f(4+h) - f(4)) ÷ ((4+h) - 4)

=(3(4+h) - 3h) ÷ (4+h - 4)

= (12+3h-12) ÷ h

= 3h ÷ h

= 3

So at all h

h = 0.01

h = 0.001

And h = 0.0001, the average rate of change of function f(x) = 3x over the interval [4,4+h] is 3.