Question

Qt find the intervals in which
the function
given by
f(x) = Sin 2. tolm ,0 <x> 2
is
Strictly gncueasing
stichly decreasing
9​

Answer 1

Answer:

f(x)=sinx+cosx

f

′

(x)=cosx−sinx

f

′

(x)=0

cosx−sinx=0

tanx=1

x=

4

π

,

4

5π

,a & 0≤x≤2π

The point x=

4

π

and

4

5π

divides, the interval [0,2π] into 3 disjoint intervals.

i.e., [(0,

4

π

),(

4

π

,

4

5π

),(

4

5π

,2π)]

f

′

(x)>0 if x∈[(0,

4

π

)∪(

4

5π

,2π)]

or f is in the intervals.

[(0,

4

π

),(

4

5π

,2π)]

Also, f

′

(x)<0, if x∈(

4

π

,

4

5π

)

So fxn is strictly decreasing in (

4

π

,

4

5π

).