What is the extreme x^{4/3}(7x^2+10x-210) ?

The extreme x^{4/3}(7x^2+10x-210) is Minimum(-4,-552*4^{1/3}),Maximum(0,0),Minimum(3,-351*3^{1/3})

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extreme x^{4/3}(7x^2+10x-210)

extreme

Minimum (- 4, - 552 \cdot 4^{\frac{1}{3}}), Maximum (0, 0), Minimum (3, - 351 \cdot 3^{\frac{1}{3}})

Solution steps

f^{'} (x) = \frac{70 x ^{\frac{1}{3}} ( x - 3 ) ( x + 4 )}{3}

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 4

into

x^{\frac{4}{3}} (7 x^{2} + 10 x - 210) : - 552 \cdot 4^{\frac{1}{3}}

Minimum (- 4, - 552 \cdot 4^{\frac{1}{3}})

Plug

x = 0

into

x^{\frac{4}{3}} (7 x^{2} + 10 x - 210) : 0

Maximum (0, 0)

Plug

x = 3

into

x^{\frac{4}{3}} (7 x^{2} + 10 x - 210) : - 351 \cdot 3^{\frac{1}{3}}

Minimum (3, - 351 \cdot 3^{\frac{1}{3}})

Minimum (- 4, - 552 \cdot 4^{\frac{1}{3}}), Maximum (0, 0), Minimum (3, - 351 \cdot 3^{\frac{1}{3}})

What is the extreme x^{4/3}(7x^2+10x-210) ?
The extreme x^{4/3}(7x^2+10x-210) is Minimum(-4,-552*4^{1/3}),Maximum(0,0),Minimum(3,-351*3^{1/3})