Answer:
Step-by-step explanation:
We will apply the definition of the derivative. Then we use algebra to expand and simplify the numerator. Next, we can cancel a factor of
h
in the numerator and denominator since
h
is approaching zero but not actually equal to zero. Finally, we can simply substitute zero for
h
to evaluate the limit.
f
′
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
=
lim
h
→
0
(
x
+
h
)
2
−
2
(
x
+
h
)
+
3
−
(
x
2
−
2
x
+
3
)
h
=
lim
h
→
0
2
x
h
−
2
h
+
h
2
h
=
lim
h
→
0
2
x
−
2
+
h
=
2
x
−
