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KEAM 2016 Math Paper
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© examsnet.com
Question : 99
Total: 120
The slope of the curve
y
=
e
x
c
o
s
x
,
x
∈
(
−
π
,
π
)
is maximum at
x
=
π
2
x
=
−
π
2
x
=
π
4
x
=
0
x
=
π
3
Validate
Solution:
Let
m
be the slope of the tangent to the curve
y
=
e
x
cos
x
Then,
m
=
d
y
d
x
=
e
x
(
cos
x
−
sin
x
)
d
m
d
x
=
e
x
(
cos
x
−
sin
x
)
+
e
x
(
−
sin
x
−
cos
x
)
=
−
2
e
x
sin
x
and
d
2
m
d
x
2
=
−
2
e
x
(
sin
x
+
cos
x
)
∴
d
m
d
x
=
0
⇒
sin
x
=
0
⇒
x
=
0
Clearly,
d
2
m
d
x
2
<
0
,
for
x
=
0
© examsnet.com
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