What is the extreme f(x)=-3/16 x^{8/3}+3/4 x^{2/3} ?

The extreme f(x)=-3/16 x^{8/3}+3/4 x^{2/3} is Maximum(-1, 9/16),Minimum(0,0),Maximum(1, 9/16)

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extreme f(x)=-3/16 x^{8/3}+3/4 x^{2/3}

extreme points

f (x) = - \frac{3}{16} x^{\frac{8}{3}} + \frac{3}{4} x^{\frac{2}{3}}

Maximum (- 1, \frac{9}{16}), Minimum (0, 0), Maximum (1, \frac{9}{16})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

- \frac{3}{16} x^{\frac{8}{3}} + \frac{3}{4} x^{\frac{2}{3}} : \frac{9}{16}

Maximum (- 1, \frac{9}{16})

Plug

x = 0

into

- \frac{3}{16} x^{\frac{8}{3}} + \frac{3}{4} x^{\frac{2}{3}} : 0

Minimum (0, 0)

Plug

x = 1

into

- \frac{3}{16} x^{\frac{8}{3}} + \frac{3}{4} x^{\frac{2}{3}} : \frac{9}{16}

Maximum (1, \frac{9}{16})

Maximum (- 1, \frac{9}{16}), Minimum (0, 0), Maximum (1, \frac{9}{16})

2 sin (x) - cos (x) - 4 x

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f (x) = 300 x - x^{2}

y = x^{3} - 2 x^{2} + x + 1

f (x) = x (15 - 43 + 2 x) (\frac{43}{2} - x)

What is the extreme f(x)=-3/16 x^{8/3}+3/4 x^{2/3} ?
The extreme f(x)=-3/16 x^{8/3}+3/4 x^{2/3} is Maximum(-1, 9/16),Minimum(0,0),Maximum(1, 9/16)