How do you find the absolute minimum for this graph?

Question

Without being given a single point of f(x), how can you know which one it is?

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Answer 1 · 2017-05-04T17:29:39

E 2

The function is increasing on #(0,1)#.

The values increase from #f(0)# to #f(1)#

The amount of the increase is the are under the graph of #f'# between #0# and #1#. This is the meaning of the net change theorem.

From #1# to #2# #f# decreases and the amount of the decrease is the area between the graph of #f'# and the #x#-axis.

Because this area appears greater than that on #[0,1]# I conclude that

#f(2)-f(1) > f(1)-f(0)# so #f(2) < f(0)#