Question

What is the range of 2sin x + 3cos x?​

Answer 1

Answer:

√13

Step-by-step explanation:

y= 2sinx+3cosx

dy/dx=2cosx-3sinx

For maxima or minima put dy/dx=0

2cosx-3sinx=0. or. 2cosx=3sinx

or. tanx=2/3. , or. sinx=2/√13. or cosx=3/√13.

d2y/dx^2=-2.sinx-3cosx=-(2sinx+3cosx)

d2y/dx^2 is - ve at x=tan-1(2/3).

There exist maxima.

Maximum value=2.2/√13+3.3/√13=13/√13= √13 units

Hope it helps! Cheers!