What is the extreme f(x)=(5-x)^{2/3}(1+x)^{1/3} ?

The extreme f(x)=(5-x)^{2/3}(1+x)^{1/3} is Maximum(1,2*2^{2/3}),Minimum(5,0)

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extreme f(x)=(5-x)^{2/3}(1+x)^{1/3}

extreme

Maximum (1, 2 \cdot 2^{\frac{2}{3}}), Minimum (5, 0)

Solution steps

f^{'} (x) = \frac{- x + 1}{( - x + 5 ) ^{\frac{1}{3}} ( x + 1 ) ^{\frac{2}{3}}}

Find intervals:

Increasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 1

into

(5 - x)^{\frac{2}{3}} (1 + x)^{\frac{1}{3}} : 2 \cdot 2^{\frac{2}{3}}

Maximum (1, 2 \cdot 2^{\frac{2}{3}})

Plug

x = 5

into

(5 - x)^{\frac{2}{3}} (1 + x)^{\frac{1}{3}} : 0

Minimum (5, 0)

Maximum (1, 2 \cdot 2^{\frac{2}{3}}), Minimum (5, 0)

What is the extreme f(x)=(5-x)^{2/3}(1+x)^{1/3} ?
The extreme f(x)=(5-x)^{2/3}(1+x)^{1/3} is Maximum(1,2*2^{2/3}),Minimum(5,0)