Math, asked by sai6129student, 18 days ago

the set of all values of f(x)=1/3sin^ 2 x+sinx cosx+cos^ 2x is

Answers

Answered by poonamsingh3461
0

Answer:

f(x)=(a

2

=−3a+2)(cos

2

x/4−sin

2

x/4)+(a−1)x+sin1

⇒f(x)=(a−1)(a−2)cosx/2+(a−1)x+sin1

⇒f

(x)=−

2

1

(a−1)(a−2)sin

2

x

+(a−1)

⇒f

(x)=(a−1)[1−

2

(a−2)

sin

2

x

]

If f(x) does not possess critical points, then f

(x)

=0 for any xϵR

⇒(a−1)[1−

2

(a−2)

sin

2

x

]

=0 for any xϵR

⇒a

=1 and 1−(

2

a−2

)sin

2

x

=0

must not have any solution in R.

⇒a

=1 and sin

2

x

=

a−2

2

is not solvable in R.

⇒a

=1 and

a−2

2

>1 [For a=2,f(x)=x+sin1∴f

(x)=1

=0]

⇒a

=1 and ∣a−2∣<2⇒a

=1 and −2<a−2<2

⇒a

=1 and 0<a<4⇒aϵ(0,1)∪(1,4).

Step-by-step explanation:

follow

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