critical numbers

[trigfun]

Hello,

I have this problem and I'm not sure how to solve it.

Find the critical numbers of the function on the interval 0 ≤ θ < 2π.
g(θ) = 4 θ - tan(θ)

θ =
(smallest value)
θ =

θ =

θ =
(largest value)

My question is pretty basic, I think. Do I use the product rule to deal with 4θ ? (I've approached it in a couple of different way but keep getting wrong answers. I just wanted to see if I'm even using the correct approach) And is the derivative of θ in this case 1 or θ ?

 

[pka]

\(g^{\prime}(\theta)=4-\sec^2(\theta)\)

 

[trigfun]

Thank you

 

[Steven G]

You can use the product rule for 4theta but I would use the constant multiple rule for derivative. You can watch a video by nothing but math proofs on youtube by going here

 

[HallsofIvy]

To use the "product rule" when one of the factors is a constant is "overkill" because the derivative of a constant is 0-
for example, using the product rule on cf(x) gives (cf(x))'= c'f(x)+ cf'(x)= 0f(x)+ cf'(x)= cf'(x). Even prior to the product rule, you should have learned that the derivative of cf(x), where c is a constant, is c times the derivative of f.