Question

Find the average rate of change of f(x) = 8x2 – 3 on the interval [1, t]. Your answer will be anexpression involving t

Answer 1

ANSWER;

The average rate of change of the function over the given interval is 8(t+1)

EXPLANATION;

The average rate of change of a given function over the interval [a,b] can be represented as;

`(f(b)-f(a))/(b-a)`

With respect to the question given, a = 1 and b = t

`\begin{gathered} f(b)=f(t)=8(t)^2-3=8t^2-3 \\ f(a)=f(1)=8(1)^2-3\text{ = 8-3 = 5} \end{gathered}`

Now, we substitute the expressions in the given rate of change relation above as follows;

`\begin{gathered} (8t^2-3-(5))/(t-1)\text{ = }(8t^2-8)/(t-1)\text{ = }(8(t^2-1))/(t-1) \\ \\ =\text{ }(8(t-1)(t+1))/(t-1)\text{ = 8(t+1)} \end{gathered}`