Question

The difference between the greatest and least values of the function 

Solution

Correct option is

9/4

The given function is periodic, with period 2π. So the difference between the greatest and least values of the function is the difference these values on the interval [0, 2π]. We have

             

 

                             

Hence x = 0, 2π/3, π and 2π are the critical points. Also, f (0) = 1 + 1/2 – 1/3 = 7/6, f (2π/3) = –13/12, f (π) = –1/6 and f (2π) = 7/6. Hence the greatest value is 7/6 and the least value is – 13/12. Thus

the  difference is

   

SIMILAR QUESTIONS

Q1

The length of a longest interval in which the function 3 sin x – 4Sin3x is increasing is

Q3

The equation e 1 + x – 2 = 0 as 

Q4

The function f satisfying 

Q5

Suppose f is differentiable on R and a ≤ f’(x) ≤ b for all x ∈ R where ab> 0. If f (0) = 0, then

Q6

The minimum value of (x) = 

Q7

, for every real number, then minimum value of f

Q8

The image of the interval [–1, 3] under the maping f(x) = 4x3 – 12x is.

Q9

 and x = 2, then