find the maximum value of

Question

f(x)= 3cos(x)-2sin(x)

I know you have to take the derivative but after the derivative I don't know how to solve it.

f'(x)=-3sin(x)-2cos(x)=0

I don't know what to do after this please help

Answer 1

so, solve the equation for f'. You have

3sinx = -2cosx
tanx = -2/3

So, that gives you x for maximum value of f(x). Just plug it in and evaluate f(x).

Of course, you need to recall how to take

sin(arctan(x)) and cos(arctan(x))

But that's just trig, right?

Or, note that

f(x) = -√13 sin(x-θ)

where tanθ = 3/2

Its amplitude is clearly √13