Is f ( x ) = x 4 − x decreasing at x = 4?I am solving a single variable calculus problem and it asks me to determine the decreasing and decreasing intervals of the function f ( x ) = x 4 − x . It's pretty clear that from ] − ∞ , 8 3 [ the function is increasing but, since the domain of the function goes only until x = 4, should I write that the decreasing interval of the function is ] 8 3 , 4 [ or ] 8 3 , 4 ] ?

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Is   f  (  x  )  =  x      4    −    x   decreasing at   x  =  4?I am solving a single variable calculus problem and it asks me to determine the decreasing and decreasing intervals of the function   f  (  x  )  =  x      4    −    x  . It&#039;s pretty clear that from       ]    −    ∞    ,          8      3        [   the function is increasing but, since the domain of the function goes only until   x  =  4, should I write that the decreasing interval of the function is       ]          8      3        ,    4    [   or       ]          8      3        ,    4    ]  ?

beentjie8e · Accepted Answer

Step 1The derivative of your function f is       f    ′    (  x  )  =      4    −    x    −      x          2              4        −        x              =            8      −      3      x              2              4        −        x             for   x  &amp;lt;  4 (no differentiability at 4).Step 2The point   x  =  8      /    3 is a local maximum. Hence the function is decreasing over   [  8      /    3  ,  4  ] because, for every   x  ,  y  ∈  [  8      /    3  ,  4  ], if   x  &amp;lt;  y then   f  (  x  )  &amp;gt;  f  (  y  ).The function is increasing over   (  −  ∞  ,  8      /    3  ].

Is f(x)=x sqrt{4-x} decreasing at x=4?

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