Question

Let f(t)=t(4-t)^(1/2) on the interval [-1,3] . Find the absolute maximum and absolute minimum of on this interval.

Answer 1

\[f(t)=t\sqrt{4-t}\]?

Answer 2

take the derivative... set it equal to 0, also check the undefined part..

Answer 3

and the endpoints

Answer 4

yes

Answer 5

\[f'(t)=\sqrt{4-t}-\frac{t}{2\sqrt{4-t}}\]
\[f'(t)=\frac{2(4-t)-t}{2\sqrt{4-t}}\]
\[f'(t)=\frac{8-3t}{2\sqrt{4-t}}\]

Answer 6

set numerator =0 and solve to find the critical point

Answer 7

ok thanks

Answer 8

thank you I really appreciate your help