# Math

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Find the maximum value of f(x)=5x^(2/3)-x^(5/3) on [1,4].

thank you!

• Math -

f' = 10/3 x^(-1/3) - 5/3 x^(2/3)
= 5/3 x^(-1/3) * (2-x)

so, a max/min occurs in this interval only at x=2.

f(1) = 4
f(2) = 4.7
f(4) = 2.5

so I'd say it's a max

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