The difference between the greatest and least values of the function f ( x ) = - x + sin 2 x on - π 2 ,…

The difference between the greatest and least values of the function f(x)=-x+sin2x on -π2,π2 is

  1. 3+2?
  2. 3+22+π6
  3. π2+π2
  4. 32-π6

Solution

f(x)=-x+sin2x

in -π2,π2

f'(x)=2cos2x-1=0

⇒x=±π6

f(x) increasing in x∈-π6,π6

decreasing in x∈-π2,-π6∪π6,π2

f(x)maximum at x=-π2 or π6

f-π2=π2

f(x)minimum at x=π2

fπ2=-π2

So, π2+π2=π

Asked in: AP EAMCET 2020 (23 Sep Shift 1)

Practice more Applications of Derivatives questions on Aicharya