Find the exact location of all the relative and absolute extrema of the function. (Order your answers from smallest to largest x.)
f(x) = 25sqr(x)*(x − 1); x ≥ 0
I found that f has relative maximum at (x, y) = (0,0)
but can't figure the absolute minimum

Question

Find the exact location of all the relative and absolute extrema of the function.  (Order your answers from smallest to largest x.)
f(x) = 25sqr(x)*(x − 1); x ≥ 0
I found that f has relative maximum at (x, y) = (0,0)
but can't figure the absolute minimum

ranga · Answer

$$f(x) = 25\sqrt{x}(x-1)~~or~~25\sqrt{x(x-1)}~~~?$$

anonymous · Answer

the first one

ranga · Answer

$$f'(x) = \frac{ 3x-1 }{ 2\sqrt{x} }$$

ranga · Answer

f'(x) = 0 when x = 1/3.  
Relative minimum at x = 1/3
f(1/3) = 25 * 1/ sqrt(3) * (-2/3) = -50/9 * sqrt(3).
This is also the absolute minimum.

ranga · Answer

x = 0 is the left end point of the domain of this function and f'(0) is not zero.  Such points are usually not considered as a relative extrema.