The slope of the secant line containing the two points \((x, f(x))\) and \((x+h,
f(x+h))\) on the graph of a function \(y=f(x)\) may be given as
\(m_{\mathrm{sec}}=\frac{f(x+h)-f(x)}{(x+h)-x}=\frac{f(x+h)-f(x)}{h} \quad h
\neq 0\)
(a) Express the slope of the secant line of each function in terms of \(x\) and
\(h\). Be sure to simplify your answer.
(b) Find \(m_{\text {sec }}\) for \(h=0.5,0.1\), and 0.01 at \(x=1 .\) What value
does \(m_{\text {sec }}\) approach as h approaches \(0 ?\)
(c) Find an equation for the secant line at \(x=1\) with \(h=0.01\).
(d) Use a graphing utility to graph fand the secant line found in part ( \(c\) )
in the same viewing window.
Problems \(85-92\) require the following discussion of a secant line. The slope
of the secant line containing the two points \((x, f(x))\) and \((x+h, f(x+h))\)
on the graph of a function \(y=f(x)\) may be given as
\(m_{\mathrm{sec}}=\frac{f(x+h)-f(x)}{(x+h)-x}=\frac{f(x+h)-f(x)}{h} \quad h
\neq 0\)
(a) Express the slope of the secant line of each function in terms of \(x\) and
\(h\). Be sure to simplify your answer.
(b) Find \(m_{\text {sec }}\) for \(h=0.5,0.1\), and 0.01 at \(x=1 .\) What value
does \(m_{\text {sec }}\) approach as h approaches \(0 ?\)
(c) Find an equation for the secant line at \(x=1\) with \(h=0.01\).
(d) Use a graphing utility to graph fand the secant line found in part ( \(c\) )
in the same viewing window.
\(f(x)=\frac{1}{x^{2}}\)
