Find the critical values of the function f(t)=t*square root(1-t), if t

The critical values of a function are the roots of the 1st
derivative of the function.

We'll differentiate the
function with respect to t, using the product rule:

f'(t) =
sqrt(1-t) - t/2sqrt(1-t)

We'll cancel
f'(t):

f'(t) = 0

sqrt(1-t) -
t/2sqrt(1-t) = 0

2(1-t) - t =
0

We'll remove the brackets:

2
- 2t - t = 0

We'll combine like
terms:

-3t = -2

t =
2/3

The critical value of the given function
is t = 2/3.