Question

If the function f(x) =
(K sin x+2 cost) divided by
+sin x + COS X)
2) K> 1
is increasing for all values of x then
1) K <1
3) K< 2
4) K>2​

Answer 1

Answer:

K >2

Step-by-step explanation:

If the function f(x)=  

sinx+cosx

ksinx+2cosx

​  

 is strictly increasing for all values of x, then

Answer 2

Answer:

The given function is:

f(x)=

sinx+cosx

Ksinx+2cosx

Differentiating once w.r.t x and and making it greater than 0 to make it monotonically increasing we get,

⇒f

′

(x)=

(sinx+cosx)

2

(Kcosx−2sinx)(sinx+cosx)−(cosx−sinx)(Ksinx+2cosx)

⇒f

′

(x)=

(sinx+cosx)

2

Ksinxcosx+Kcos

2

x−2sin

2

x−2sinxcosx−Ksinxcosx−2cos

2

x+Ksin

2

x+2sinxcosx

⇒f

′

(x)=

(sinx+cosx)

2

Kcos

2

x+Ksin

2

x−2cos

2

x−2sin

2

x

⇒f

′

(x)=

(sinx+cosx)

2

K−2

Now, f

′

(x)>0

⇒

(sinx+cosx)

2

K−2

>0

⇒K−2>0

⇒K>2 ....