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Byju's Answer
Standard XII
Mathematics
Chain Rule of Differentiation
Find the valu...
Question
Find the values of b for which the function f(x) = sin x − bx + c is a decreasing function on R.
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Solution
f
x
=
sin
x
-
b
x
+
c
f
'
x
=
cos
x
-
b
Given:
f
x
is decreasing on
R.
f
'
x
<
0
,
∀
x
∈
R
⇒
cos
x
-
b
<
0
,
∀
x
∈
R
⇒
cos
x
-
b
<
0
,
∀
x
∈
R
⇒
cos
x
<
b
,
∀
x
∈
R
⇒
b
⩾
1
∵
-
1
⩽
cos
x
⩽
1
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