# absolute and local maximum and minimum

• Nov 18th 2009, 02:13 PM
break
absolute and local maximum and minimum
find the absolute and local maximum and minimum values of f.

$f(t) = 5cos(t)$
-pi/2 ≤ t ≤ 3pi/2

i have no clue how to solve this because cos(-π/2) and cos(3π/2) equal 0 but the answer isn't zero.
• Nov 18th 2009, 02:40 PM
skeeter
Quote:

Originally Posted by break
find the absolute and local maximum and minimum values of f.

$f(t) = 5cos(t)$
-pi/2 ≤ t ≤ 3pi/2

i have no clue how to solve this because cos(-π/2) and cos(3π/2) equal 0 but the answer isn't zero.

absolute extrema don't always occur at endpoints.

based on your prior knowledge of trig alone (w/o calculus), you should be able to sketch the relatively simple graph of $f(t)$.

based on that sketch, the absolute max for $f(t)$ is $f(0) = 5$, and the absolute min is $f(\pi) = -5$