MA 181 Computing the Derivative Graphically and Numerically
Section 2.7
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1. Let
x
xxfy == )(
(a) Draw a line tangent to the curve at the point
where x = 2. Estimate the slope of this
tangent line.
(b) Set up the difference quotient h
fhf )2()2( −+
for this function.
(c) Complete the table below.
h
h
fhf )2()2( −+
h
h
fhf )2()2(
−
+
1 -1
0.1 -0.1
0.01 -0.01
0.001 -0.001
0.0001 -0.0001
(d) Estimate h
fhf
fh
)2()2(
lim)2( 0
−
+
=
′
→ using the table values from part (c). Compare your
result to the slope estimate you made in part (a).
