At what points in the interval [0, 2π] does the function sin 2x attain its maximum value?

Solution:

Maxima and minima are known as the extrema of a function.

Maxima and minima are the maximum or the minimum value of a function within the given set of ranges.

Let f (x) = sin 2x

Therefore,

On differentiating wrt x, we get

f' (x) = 2 cos 2x

Now,

f' (x) = 0

⇒ 2 cos 2x = 0

⇒ 2x = π / 2, 3π / 2, 5π / 2, 7π / 2

⇒ x = π / 4, 3π / 4, 5π / 4, 7π / 4

Now, we evaluate the value of f at a critical point x = π / 4, 3π / 4, 5π / 4, 7π / 4 and at the endpoints of the interval [0, 2π].

Therefore,

f (π / 4) = sin π / 2

= 1

f (3π / 4) = sin 3π / 2

= - 1

f (5π / 4) = sin 5π / 2

= 1

f (7π / 4) = sin 7π / 2

= - 1

f (0) = sin 0

= 0

f (2π) = sin 2π

= 0

Hence, we can conclude that the absolute maximum value of on [0, 2π] is occurring at x = π / 4 and x = 5π / 4

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.5 Question 8

At what points in the interval [0, 2π] does the function sin 2x attain its maximum value?

Summary:

Hence, we can conclude that the absolute maximum value of on [0, 2π] is occurring at x = π / 4 and x = 5π / 4. Maxima and minima are known as the extrema of a function