Asked by Jay
Find the intervals on which the function f(x)=x²/³(10-x) is increasing and decreasing. Sketch the graph of y=f(x)and identify any local maxima and minima. Any global extrema should also be identified.
Answers
Answered by
Steve
y = x^(2/3)(10-x) = 10x^(2/3) - x^(5/3)
y' = (20/3)x^(-1/3) - (5/3)x^(2/3)
= 5/3 (4-x)/x^(1/3)
y'=0 when x=4
y increases when y'>0, or x<4
see the graph and info at
http://www.wolframalpha.com/input/?i=x^%282%2F3%29%2810-x%29
y' = (20/3)x^(-1/3) - (5/3)x^(2/3)
= 5/3 (4-x)/x^(1/3)
y'=0 when x=4
y increases when y'>0, or x<4
see the graph and info at
http://www.wolframalpha.com/input/?i=x^%282%2F3%29%2810-x%29
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