Use a CAS to perform the following steps for
Chapter 3, Problem 68CE(choose chapter or problem)
Use a CAS to perform the following steps for the functions in Exercises 63–68.
a. Plot \(y=f(x)\) to see that function’s global behavior.
b. Define the difference quotient \(q\) at a general point \(x\), with general step size \(h\).
c. Take the limit as \(h \rightarrow 0\). What formula does this give?
d. Substitute the value \(x=x_{0}\) and plot the function \(y=f(x)\) together with its tangent line at that point.
e. Substitute various values for \(x\) larger and smaller than \(x_{0}\) into the formula obtained in part (c). Do the numbers make sense with your picture?
f. Graph the formula obtained in part (c). What does it mean when its values are negative? Zero? Positive? Does this make sense with your plot from part (a)? Give reasons for your answer.
\(f(x)=x^{2} \cos x, x_{0}=\pi / 4\)
Equation Transcription:
Text Transcription:
f(x)
q
x
h
h rightarrow 0
x=x_0
y=f(x)
x
x_0
f(x)=x^2 cos x, x_0=pi/4
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