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How to find absolute extrema of 4 - abs(t - 4)

Determine the absolute extrema of the function and the x-value in the closed interval where it occurs.

h ( t ) = 4 - abs ( t - 4 )
closed interval is [ 1, 6 ]

This is not a homework problem.

This problem is from high school Advance Placement Calculus class.

SOLUTION

ozo

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SOLUTION

d-glitch

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ASKER CERTIFIED SOLUTION

phoffric

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naseeam

ASKER

h1(t) = 4 - ( t - 4 ) ; [4, 6 ]
h2(t) = 4 - ( - t + 4); [1, 4 ]

h1 ' ( t ) = - 1
h2 ' ( t ) = 1

At t = 4, slope is undefined. There is absolute maximum at t = 4.

Am I correct ?

phoffric

I hoped you first simplified h1(t) and h2(t).
You are correct.

In general, as you progress into harder functions and inequality relationships with multiple absolute value functions, the task first becomes identifying multiple partitions and then defining functions on each partition having no absolute value functions. A bit harder than this problem if the individual regions for different absolute value expressions overlap.

HainKurt

strange.. I remember I posted something here, but I dont see now... did someone delete my post?

I dont see my post but i still get notifications? what happened to my post (and possible points)?

ozo

each partition having no absolute value functions

or more generally, each partition being monotonic.