# `g(t) = tsqrt(4 - t), t < 3` Find the critical numbers of the function. You need to evaluate the critical numbers of the function and for this reason, you must differentiate the function with respect to t, using the product and chain rules, such that:

`g'(t) = (t*sqrt(4 - t))'`

`g'(t) = t'*sqrt(4 - t) + t*(sqrt(4 - t))'`

`g'(t) = sqrt(4 - t)...

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

You need to evaluate the critical numbers of the function and for this reason, you must differentiate the function with respect to t, using the product and chain rules, such that:

`g'(t) = (t*sqrt(4 - t))'`

`g'(t) = t'*sqrt(4 - t) + t*(sqrt(4 - t))'`

`g'(t) = sqrt(4 - t) + t*((4-t)')/(2sqrt(4 - t))`

`g'(t) = sqrt(4 - t) + (-t)/(2sqrt(4 - t))`

You need to solve for t the equation g'(t) = 0:

`sqrt(4 - t) + (-t)/(2sqrt(4 - t)) = 0`

`2(4 - t) - t = 0 => 8 - 2t - t = 0 => 3t = 8 => t = 8/3`

Hence, evaluating the critical values of the given function, yields `t = 8/3.`

Approved by eNotes Editorial Team