1. ## trig max/min values

hi im struggling with my homework and was wondering if anyone can help

here the question...

find the max and min values of 3sinx + 2cosx ,and find in radians ,the smallest values of x at which they occur

any help is fully appreciated thank you

2. $\frac{d}{dx}[3sin(x)+2cos(x)]=3cos(x)-2sin(x)$

Set to 0 and solve for x:

$3cos(x)-2sin(x)=0$

Now, assuming $cos(x)\neq 0$:

$\frac{sin(x)}{cos(x)}=\frac{3}{2}$

$tan(x)=\frac{3}{2}$

$x=C{\pi}-tan^{-1}(\frac{2}{3})+\frac{\pi}{2}$

Let C=0 for the smallest value for the max and C=-1 for the smallest value that is a min.

Graph it as well and take a peek.