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KEAM 2017 Math Paper
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© examsnet.com
Question : 5
Total: 120
Let f(x + y) = f(x) f(y) for all x and y. If f(0) = 1, f(3) = 3 and f ′(0) =11, then f ′(3) is equal to
11
22
33
44
55
Validate
Solution:
We have
f
′
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
⇒
f
′
(
3
)
=
lim
h
→
0
f
(
3
+
h
)
−
f
(
3
)
h
=
lim
h
→
0
f
(
3
)
f
(
h
)
−
f
(
3
+
0
)
h
=
lim
h
→
0
f
(
3
)
f
(
h
)
−
f
(
3
)
f
(
0
)
h
=
f
(
3
)
lim
h
→
0
f
(
h
)
−
f
(
0
)
h
=
f
(
3
)
lim
h
→
0
f
(
0
+
h
)
−
f
(
0
)
h
=
f
(
3
)
f
′
(
0
)
=
3
×
11
=
33
© examsnet.com
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