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Byju's Answer
Standard XII
Mathematics
Monotonically Increasing Functions
fx=cos 2x-sin...
Question
f
(
x
)
=
cos
2
x
−
sin
2
x
at
x
=
π
12
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Solution
f
(
x
)
=
cos
2
x
−
sin
2
x
c
o
s
x
cos
x
−
sin
x
sin
x
c
o
s
(
x
+
x
)
=
cos
2
x
f
(
π
12
)
=
cos
2
(
π
12
)
cos
(
π
6
)
=
√
3
2
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Similar questions
Q.
If f(x) = sin2x - cos2x, Find f
I
(π/6)
Q.
Let
f
(
x
)
=
∣
∣ ∣ ∣
∣
sin
2
x
−
2
+
cos
2
x
cos
2
x
2
+
sin
2
x
cos
2
x
cos
2
x
sin
2
x
cos
2
x
1
+
cos
2
x
∣
∣ ∣ ∣
∣
,
x
∈
[
0
,
π
]
.
Then the maximum value of
f
(
x
)
is equal to
Q.
Verify Rolle's theorem for each of the following functions on the indicated intervals
(i) f(x) = cos 2 (x − π/4) on [0, π/2]
(ii) f(x) = sin 2x on [0, π/2]
(iii) f(x) = cos 2x on [−π/4, π/4]
(iv) f(x) = e
x
sin x on [0, π]
(v) f(x) = e
x
cos x on [−π/2, π/2]
(vi) f(x) = cos 2x on [0, π]
(vii) f(x) =
sin
x
e
x
on 0 ≤ x ≤ π
(viii) f(x) = sin 3x on [0, π]
(ix) f(x) =
e
1
-
x
2
on [−1, 1]
(x) f(x) = log (x
2
+ 2) − log 3 on [−1, 1]
(xi) f(x) = sin x + cos x on [0, π/2]
(xii) f(x) = 2 sin x + sin 2x on [0, π]
(xiii)
f
x
=
x
2
-
sin
π
x
6
on
[
-
1
,
0
]
(xiv)
f
x
=
6
x
π
-
4
sin
2
x
on
[
0
,
π
/
6
]
(xv) f(x) = 4
sin
x
on [0, π]
(xvi) f(x) = x
2
− 5x + 4 on [1, 4]
(xvii) f(x) = sin
4
x + cos
4
x on
0
,
π
2
(xviii) f(x) = sin x − sin 2x on [0, π]