Find the critical numbers of the function f(x) = 4 + x/3 - x^2/2

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nees101 | Student, Graduate | (Level 2) Adjunct Educator

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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,

`` `f'(x)=1/3-x=0`

`x=1/3` , which is the critical number of the function f(x).

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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` .

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