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What are the extrema of #f(x) = 8 - 2x# for #x>=6#?

Answer 1

#f(x)# is a line with a negative slope, so on the interval #x>= 6#, the maximum is at #x=6#. There is no minimum because #f(x)# is always decreasing, and the interval given is #[6,oo]#. graph{-2x+8 [-4.25, 15.75, -7.8, 2.2]}

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Answer 2

Christopher Allers

The function ( f(x) = 8 - 2x ) for ( x \geq 6 ) has a minimum value but no maximum value within that domain. The minimum occurs at ( x = 6 ), and its value is ( f(6) = 8 - 2 \times 6 = 8 - 12 = -4 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

What are the extrema of #f(x) = 8 - 2x# for #x&gt;=6#?

What are the extrema of #f(x) = 8 - 2x# for #x>=6#?