What is the extreme (-4)/(x^3)+(30)/((10x+3)^2) ?

The extreme (-4)/(x^3)+(30)/((10x+3)^2) is Minimum(-0.24386…,371.01468…),Maximum(20.87473…,0.00022…)

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extreme (-4)/(x^3)+(30)/((10x+3)^2)

extreme points

\frac{- 4}{x ^{3}} + \frac{30}{( 10 x + 3 ) ^{2}}

Minimum (- 0.24386 \dots, 371.01468 \dots), Maximum (20.87473 \dots, 0.00022 \dots)

Solution steps

Find the critical points:

x \approx - 0.24386 \dots, x = 20.87473 \dots

Domain of

\frac{- 4}{x ^{3}} + \frac{30}{( 10 x + 3 ) ^{2}} : x < - \frac{3}{10} or - \frac{3}{10} < x < 0 or x > 0

Find intervals:

Increasing

: - \infty < x < - \frac{3}{10},

Decreasing

: - \frac{3}{10} < x < - 0.24386 \dots,

Increasing

: - 0.24386 \dots < x < 0,

Increasing

: 0 < x < 20.87473 \dots,

Decreasing

: 20.87473 \dots < x < \infty

Plug the extreme point

x = - 0.24386 \dots

into

\frac{- 4}{x ^{3}} + \frac{30}{( 10 x + 3 ) ^{2}} \Rightarrow y = 371.01468 \dots

Minimum (- 0.24386 \dots, 371.01468 \dots)

Plug the extreme point

x = 20.87473 \dots

into

\frac{- 4}{x ^{3}} + \frac{30}{( 10 x + 3 ) ^{2}} \Rightarrow y = 0.00022 \dots

Maximum (20.87473 \dots, 0.00022 \dots)

Minimum (- 0.24386 \dots, 371.01468 \dots), Maximum (20.87473 \dots, 0.00022 \dots)

(x - 2)^{3}

f (x, y) = x^{2} + y^{2} + x^{2} y^{2}

f (x) = x^{\frac{8}{9}} - 3

f (x) = x^{3} - 3 x^{2} + 3 x + 7

f (x) = (t - 4 t^{2})^{\frac{1}{3}}

What is the extreme (-4)/(x^3)+(30)/((10x+3)^2) ?
The extreme (-4)/(x^3)+(30)/((10x+3)^2) is Minimum(-0.24386…,371.01468…),Maximum(20.87473…,0.00022…)