A number a is a critical number the function f(x) if a lies in the domain of the function, and f'(a) = 0 or f'(a) is not defined.
For the function `f(x) = 4 + x/3 - x^2/2` , the first derivative `f'(x) = 1/3 - x` .
Solving f'(x) = 0 gives the equation `1/3 - x = 0`
`x = 1/3`
For `f(x) = 4 + x/3 - x^2/2` , `x = 1/3` lies in the domain of the function.
The required critical number of the function `f(x) = 4 + x/3 - x^2/2` is `x = 1/3` .
Given the function ```f(x)=4+x/3-x^2/2`
We are asked to find the critical points of this function.
Inorder to do that we have to differentiate the function with respect to x and then equate it to zero.
So we get,
`x=1/3` , which is the critical number of the function f(x).