How do you find the critical numbers of $f (t) = t {(4 - t)}^{\frac{1}{2}}$ $f(t)=t(4-t)^(1/2)$ ?

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Answer 1 · 2017-11-09T18:45:45

Please see below.

Domain of $f$ $f$ is $(- \infty, 4]$ $(-oo,4]$

$f'(t) = (8-3t)/(2sqrt(4-t))$

$f'(t) = 0$ at $t=8/3$ and $f'(t)$ does not exist at $x=4$ .

Both numbers are in the domain of $f$ , so both are critical numbers for $f$ .

How do you find the critical numbers of f(t)=t(4-t)^(1/2)f(t)=t(4−t)12 f(t)=t(4-t)^(1/2)?