1114 A function y = f(x) and values of x0 and x1 are given.(a) Find the average rate of

Chapter 2, Problem 12

(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.

\(y=x^{3} ; \ x_{0}=1, \ x_{1}=2\)

Equation Transcription:

y = f(x)

x0

x1

y

x

[x0, x1]

y = x3; x0 = 1, x1 = 2

Text Transcription:

y = f(x)

x_0

x_1

y

x

[x_0, x_1]

y = x^3; x_0 = 1, x_1 = 2