Question

Determine the absolute extrema of each function on the given interval. Illustrate your results by
sketching the graph of each function.


f(x) = (x − 1)^2 , 0 ≤ x ≤ 2

Answer 1

clearly a simple parabola

f ' (x) = 2(1-x) = 0 for a max/min
x=1
f(1) = (1-1)^2 = 0

endpoints:
f(0) = (-1)^2 = 1
f(2) = (162 = 1

parabola opens up, so the minimum is 0 when x = 1

or
(the vertex is (1,0) )

You have posted several of these rather straightforward problems. What is it exactly that you are having difficulties with ?