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

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

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

extreme

Minimum (0, 3), Maximum (2, - 1)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

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

Minimum (0, 3)

Plug

x = 2

into

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

Maximum (2, - 1)

Minimum (0, 3), Maximum (2, - 1)

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