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

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

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extreme (2x)/3+(x+1)^{2/3}

extreme points

\frac{2 x}{3} + (x + 1)^{\frac{2}{3}}

Maximum (- 2, - \frac{1}{3}), Minimum (- 1, - \frac{2}{3})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < - 1,

Increasing

: - 1 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, - \frac{1}{3})

Plug

x = - 1

into

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

Minimum (- 1, - \frac{2}{3})

Maximum (- 2, - \frac{1}{3}), Minimum (- 1, - \frac{2}{3})

f (x) = \frac{2 x ^{3} - 6}{9}

f (x) = \frac{x + 7}{x - 5}

f (x) = 2 (y - 1) (y - 2) (y - 3)

3 sin (\frac{2 π θ}{5})

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