22.0k views
0 votes
Consider the function f(x) = 1/x on the interval [1, 10] Find the average or mean slope of the function on this interval.

Consider the function f(x) = 1/x on the interval [1, 10] Find the average or mean-example-1

1 Answer

4 votes

We will have the following:

First, we determine the equation for the slope, that is:


f(x)=(1)/(x)\Rightarrow f^(\prime)(x)=-(1)/(x^2)

Now, to determine the average slope we examine the slopes at the edges:


\begin{gathered} f^(\prime)(1)=-(1)/(1^2)\Rightarrow f^(\prime)(1)=-1 \\ \\ and \\ \\ f^(\prime)(10)=-(1)/((10)^2)\Rightarrow f^(\prime)(10)=-(1)/(100) \end{gathered}

So, the average slope will be given by:


\begin{gathered} m_a=((-(1)/(100))+(-1))/(2)\Rightarrow m_a=-(101)/(200) \\ \\ \Rightarrow m_a=-0.505 \end{gathered}

So, the average slope in that interval is -0.505.

Now, we determine the exact point where the slope is that, that is:


\begin{gathered} -0.505=-(1)/(x^2)\Rightarrow x^2=(1)/(0.505) \\ \\ \Rightarrow x=\sqrt{(1)/(0.505)}\Rightarrow x=1.407195089... \\ \\ \Rightarrow x\approx1.4 \end{gathered}

So, the exact point is sqrt( 1 / 0.505), that is approximately 1.4.

User Gwcoffey
by
9.4k 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