Given a function, f ( x ) = 4 x − x 2 , what does it mean to find its critical points?Assuming that the domain of the function in question is not explicitly stated, are we right to say that this function is well-defined only when 0 ≤ x ≤ 4?

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Given a function,  f  (  x  )  =      4    x    −          x      2      , what does it mean to find its critical points?Assuming that the domain of the function in question is not explicitly stated, are we  right to say that this function is well-defined only when   0  ≤  x  ≤  4?

erlentzed · Accepted Answer

When dealing with functions of a real variable, a critical point is a point in the domain of the function where the function is either not differentiable or the derivative is equal to zeroIn our case the function is not differentiable in   x  =  0 and   x  =  4. On the other hand:      f    ′    (  x  )  =            2      −      x              4      x      −              x                  2                    Therefore       f    ′    (  x  )  =  0 only if   x  =  2, that critical point would correspond to the maximum of the function in the domain   x  ∈  [  0  ,  4  ]

Given a function,f(x)=sqrt (4x−x^2), what does it mean to find its critical points? Assuming that the domain of the function in question is not explicitly stated, are we right to say that this function is well-defined only when 0<=x<=4?

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