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Tardigrade
Question
Mathematics
The value of K in order that f(x)= sin x- cos x-K x+5 decreases for all positive real values of x is given by
Q. The value of
K
in order that
f
(
x
)
=
sin
x
−
cos
x
−
K
x
+
5
decreases for all positive real values of
x
is given by
1780
229
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Application of Derivatives
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A
K
<
1
8%
B
K
≥
1
19%
C
K
>
2
66%
D
K
<
2
7%
Solution:
We have,
f
(
x
)
=
sin
x
−
cos
x
−
K
x
+
5
⇒
f
′
(
x
)
=
cos
x
+
sin
x
−
K
For decreasing,
f
′
(
x
)
<
0
⇒
cos
x
+
sin
x
−
K
<
0
⇒
K
>
cos
x
+
sin
x
⇒
K
>
2
[
2
1
cos
x
+
2
1
sin
x
]
⇒
K
>
2
sin
(
4
π
+
x
)
∴
K
>
2