Question

The maximum value of sin x cos x is

A. 1/4

B. 1/2

C. √2

D. 2√2

Answer 1

Let f(x)= sin x cos x

But we know sin2x=2sin x cos x

⇒ f’(x)=cos2x……(i)

Putting f’(x)=0,we get critical points as

cos2x=0

Now we will find out the second derivative by deriving equation (i), we get

⇒ f’’ (x)=-sin 2x.2

⇒ f’’(x)=-2sin2x

Now we will find the value of f’’(x) at  x = π/4, we get

Therefore at x = π/4, f(x) is maximum and π/4 is the point of maxima.

Now we will find the maximum value of sin x cos x by substituting x = π/4, in f(x), we get

f(x)= sin x cos x

Hence the maximum value of sin x cos x is 1/2

So the correct option is option B.