SOLUTION: Determine the location and value of the absolute extreme values of f on the given interval, if they exist. f(x) = 4x^3/4 −x on [0,256]

Question 1158618: Determine the location and value of the absolute extreme values of f on the given interval, if they exist.
f(x) = 4x^3/4 −x on [0,256]

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!

(0, 0) is one possible extreme value
at x=256, 4*(4^4)^(3/4)-x or 4*4^3-256 which is also 0.
so the two ends of the graph (0, 0) and (256, 0) give the lowest values of the function.
the greatest value comes in between and is a maximum
the derivative is (3/4)*4(x^(-1/4))-1 and set equal to 0 and move the -1
3x^(-1/4)=1
3=x^(1/4)
x=81, raising both sides to the fourth power
at that value, f(x)=108-81=27
(81, 27)
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