Home
Class 12
MATHS
Separate [0, (pi)/(2)] into subintervals...

Separate `[0, (pi)/(2)]` into subintervals in which `f(x) = sin 3x` is (a) increasing (b) decreasing

Text Solution

AI Generated Solution

To solve the problem of separating the interval \([0, \frac{\pi}{2}]\) into subintervals where the function \(f(x) = \sin(3x)\) is increasing and decreasing, we will follow these steps: ### Step 1: Find the derivative of the function We start by differentiating the function \(f(x) = \sin(3x)\). \[ f'(x) = \frac{d}{dx}(\sin(3x)) = 3\cos(3x) \] ...
Promotional Banner

Similar Questions

Explore conceptually related problems

Separate [0,pi/2] into subintervals in which f(x)=sin3x is increasing or decreasing.

Find the intervals in which f(x) = sin 3x, x in [0,pi/2] is (i) increasing, (ii) decreasing.

Find the intervals in which f(x)=sin3x cos3x,0

Separate the interval [0,pi/2] into sub- intervals in which f(x)=s in^(4)x+cos^(4)x is increasing or decreasing.

Find the intervals in which f(x)=sinx+|sinx|, 0

Find the intervals in which f(x)=s in x(1+cosx), 0

Find the intervals in which f(x)=5+36x+3x^(2)-2x^(3) is increasing or decreasing.

Find the intervals in which f(x)=8+36x+3x^(2)-2x^(3) is increasing or decreasing.

Find the intervals in which f(x)=6+12x+3x^(2)-2x^(3) is increasing or decreasing.

Find the intervals in which f(x)=5x^(3/2)-3x^(5/2),x>0 is increasing or decreasing.