Question

y=4-2cosx then what is tha maximum value of y
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Answer 1

Answer:

Given y=2cos2x−cos4x

⇒

dx

dy

=−4sin2x+4sin4x

For maxima or minima

dx

dy

=0

⇒4(sin4x−sin2x)=0

⇒4(2sin2xcos2x−sin2x)=0

⇒4sin2x(2cos2x−1)=0

⇒sin2x=0 or 2cos2x−1=0

Now, sin2x=0⇒2x=0,π,2π⇒x=0,

2

π

,π

2cos2x−1=0⇒cos2x=

2

1

⇒2x=

3

π

,

3

5π

⇒x=

6

π

,

6

5π

Min value =−3

Max value =

2

3