How do you locate the absolute extrema of the function on the closed interval #y = 3 - abs(x - 3)#, on the interval [-1, 5]?

1 Answer
Skewd
Jun 21, 2018

Find the first derivative and any critical values.
Find the y-value for each critical value and the y-value at the endpoints. The largest is abs. max, the smallest is abs min.

Explanation:

Note, the graph of any absolute value equation has a V shape, this one is upside down, shifted right 3 units and up 3 units. The corner of the V is at x = 3.
#f(-1)=-1# the absolute min
#f(3)=3# the absolute max
#f(5)=1#

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