Question

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

Solution

Correct option is

π/3

Since 3 sin x – 4 sin3x = sin 3x and sin 3x increases when 3x takes values from –π/2 to π/2 or x takes value from π/6 to π/6. Thus, the length of the longest interval in which 3 sinx – 4 sin3x increases is π/6 – (π/6) = π/3.

SIMILAR QUESTIONS

Q1

The equation of the common tangent to the curves y2 = 8x and xy = –1 is 

 

Q2

If ab > 0 then the minimum value of  

Q3

The curve y = ax3 + bx2 + cx + 8 touches x – axis at P(2, 0) and cuts they – axis at a point Q where its gradient is 3. The value of a, b, c are respectively

Q4

If the tangent at (1, 1) on y2 = x(2 – x)2 meets the curve again at P, is

Q5

The tangent to the curve 

At the point corresponding to  is

Q6

The points of contact of the vertical tangents to x = 2 – 3 sinθ,  y = 3 + 2 cos θ are

Q7

 the in this interval

Q8

The set of all values of a for which the function

                   

decreases for all real x is

Q9