1114 A function y = f(x) and values of x0 and x1 are given.(a) Find the average rate of
Chapter 2, Problem 13(choose chapter or problem)
A function \(y = f(x)\) and values of \(\mathrm{x}_{0}\) and \(\mathrm{x}_{1}\) are given.
(a) Find the average rate of change of \(y\) with respect to \(x\) over the interval \(\left[\mathrm{x}_{0}, \mathrm{x}_{1}\right]\).
(b) Find the instantaneous rate of change of \(y\) with respect to \(x\) at the specified value of \(\mathrm{x}_{0}\).
(c) Find the instantaneous rate of change of \(y\) with respect to \(x\) at an arbitrary value of \(\mathrm{x}_{0}\).
(d) The average rate of change in part (a) is the slope of a certain secant line, and the instantaneous rate of change in part (b) is the slope of a certain tangent line. Sketch the graph of \(y = f(x)\) together with those two lines.
\(y=1 / x ; \ x_{0}=2, \ x_{1}=3\)
Equation Transcription:
y = f(x)
x0
x1
y
x
[x0, x1]
y = 1/x; x0 = 2, x1 = 3
Text Transcription:
y = f(x)
x_0
x_1
y
x
[x_0, x_1]
y = 1/x; x_0 = 2, x_1 = 3
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