172k views
1 vote
Find the average rate of change for f(t) =6 t^2 + 10 over the interval [3,3+h]

1 Answer

3 votes

The formula for the average rate of change from point a to point b is:


R=(f(b)-f(a))/(b-a)

In our case:


\begin{gathered} a=3 \\ b=3+h \\ f(t)=6t^2+10 \end{gathered}

Let's evaluate the function for a and b:


\begin{gathered} f(a)=f(3)=6\cdot(3)^2+10=6\cdot9+10=54+10 \\ f(a)=64 \end{gathered}
\begin{gathered} f(b)=f(3+h)=6\cdot(3+h)^2+10=6\cdot(9+6h+h^2)+10 \\ f(b)=54+36h+6h^2+10 \\ f(b)=6h^2+36h+64 \end{gathered}

Now, putting into the rate equation:


\begin{gathered} R=(f(b)-f(a))/(b-a) \\ R=(6h^2+36h+64-64)/(3+h-3) \\ R=(6h^2+36h)/(h) \\ R=(h(6h+36))/(h) \\ R=6h+36 \end{gathered}

User Sarela
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories