Locate the absolute extrema of the following function of the interval ( 0, 4 ). f ( x ) = x 3 − 12 x

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Locate the absolute extrema of the following function of the interval ( 0, 4 ).  f  (  x  )  =      x          3        −  12  x

wijnvatid · Accepted Answer

To find the absolute extrema, take the derivative and set it to 0:      f    ′    (  x  )  =  3      x          2        −  12  =  0.  3      x          2        =  12.      x          2        =  4.  x  =  ±  2. Since x=-2 is not on the interval, throw it out. Sothe absolute extremum is at x=2. y can be determined bysubstitution.   y  =      2          3        −  24  =  −  16. If you substitute x=0 intothe equation, y=0. If you substitute x=4 into the equation, y=16.In either case, they are both higher values than y=-16. So there isan absolute minimum at the point (2, -16)

Locate the absolute extrema of the following function of the interval ( 0, 4 ). f(x)=x^3 -12x

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