calculus
posted by help!! .
find the absolute minimum and maximum values of f(x)=x^(1/3) (3+x) on the interval [2,1]

f' = (4x+3)/(3x^(2/3))
This is undefined at x=0, where f(0) = 0, a local min.
f'=0 at x = 3/4 where there is a local max. f(3/4) = (9/4) ∛(3/4)
check the value of f at the end points for other max/min values. 
do not get it :(

what don't you get?
max/min occurs where f' = 0, as long as f" is not also zero
where f' is undefined, check to see whether f is defined there. If so, it will be some kind of cusp, so a max or min. Or it will have a vertical tangent.
As it turns out, I made a mistake at x=0; there is no local min there.
And, the extremum at x = 3/4 is a min, not a max.
Oddly, this error was caused by my trust in the graphs at wolframalpha.com, which showed it wrong.
To see the real graph, visit
http://rechneronline.de/functiongraphs/
Respond to this Question
Similar Questions

Calculus
Find the absolute maximum and absolute minimum values of f(x)=sinx + (ã3) cosx on the closed interval [0,ƒÎ/3] 
Calculus (pleas help!!!)
Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter 1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum … 
Calculus (pleas help!!!)
Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter 1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum … 
Calculus
Find the absolute maximum and absolute minimum values of the function f(x)=x^3+6x^263x+4 on each of the indicated variables. Enter DNE for does not exist. (A) Interval = [8,0] Absolute maximum = Absolute minimum = (B) Interval = … 
Calculus
Find the absolute minimum and absolute maximum values of f on the interval below. f(x) = x4  8x2 + 6 [3, 4] 
Calculus
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = (x2  1)3 [1, 6] 
Calculus
Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 8 cos t + 4 sin 2t, [0, π/2] 
calculus
2) Let g(s)= t(4−t)^1/2 on the interval [0,2]. Find the absolute maximum and absolute minimum of g(t) on this interval. Enter DNE if the absolute maximum or minimum does not exist. The absolute max occurs at t= . The absolute … 
Calculus 1
Find the absolute maximum and absolute minimum values of f on the given interval. f(x)=(x^24)/(x^2+4), [4,4] 
Calculus 1
Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 16 cos t + 8 sin 2t, [0, π/2]