Question

For the function
f
(
x
)
=
3
(
x
+
2
)
2
and the point
P
given by
x
=
−
3
answer each of the following questions.
For the points
Q
given by the following values of
x
compute (accurate to at least 8 decimal places) the slope,
m
P
Q
, of the secant line through points
P
and
Q
.
-3.5 -3.1 -3.01 -3.001 -3.0001
-2.5 -2.9 -2.99 -2.999 -2.9999
Use the information from (a) to estimate the slope of the tangent line to
f
(
x
)
at
x
=
−
3
and write down the equation of the tangent line.
Solution