What is the extreme ((12x^3))/3+38x^2+56x,-8<= x<= 1 ?

The extreme ((12x^3))/3+38x^2+56x,-8<= x<= 1 is

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extreme ((12x^3))/3+38x^2+56x,-8<= x<= 1

extreme points

\frac{( 12 x ^{3} )}{3} + 38 x^{2} + 56 x, - 8 \leq x \leq 1

Minimum (- 8, - 64), Maximum (- \frac{19 + 193}{6}, \frac{2071 + 193 193}{27}), Minimum (\frac{- 19 + 193}{6}, \frac{2071 - 193 193}{27}), Maximum (1, 98)

Solution steps

Find the critical points:

x = - 8, x = - \frac{19 + 193}{6}, x = \frac{- 19 + 193}{6}, x = 1

Domain of

\frac{12 x ^{3}}{3} + 38 x^{2} + 56 x, - 8 \leq x \leq 1 : - 8 \leq x \leq 1

Find intervals:

Increasing

: - 8 < x < - \frac{19 + 193}{6},

Decreasing

: - \frac{19 + 193}{6} < x < \frac{- 19 + 193}{6},

Increasing

: \frac{- 19 + 193}{6} < x < 1

Plug the extreme point

x = - 8

into

\frac{12 x ^{3}}{3} + 38 x^{2} + 56 x \Rightarrow y = - 64

Minimum (- 8, - 64)

Plug the extreme point

x = - \frac{19 + 193}{6}

into

\frac{12 x ^{3}}{3} + 38 x^{2} + 56 x \Rightarrow y = \frac{2071 + 193 193}{27}

Maximum (- \frac{19 + 193}{6}, \frac{2071 + 193 193}{27})

Plug the extreme point

x = \frac{- 19 + 193}{6}

into

\frac{12 x ^{3}}{3} + 38 x^{2} + 56 x \Rightarrow y = \frac{2071 - 193 193}{27}

Minimum (\frac{- 19 + 193}{6}, \frac{2071 - 193 193}{27})

Plug the extreme point

x = 1

into

\frac{12 x ^{3}}{3} + 38 x^{2} + 56 x \Rightarrow y = 98

Maximum (1, 98)

Minimum (- 8, - 64), Maximum (- \frac{19 + 193}{6}, \frac{2071 + 193 193}{27}), Minimum (\frac{- 19 + 193}{6}, \frac{2071 - 193 193}{27}), Maximum (1, 98)

- x^{3} + 27 x - 58

y = x^{3} + 2 x

f (x) = 2 x^{3} - 42 x^{2} + 270 x + 10

y = 6 x^{3} + 72 x^{2} + 270 x

\frac{( 4 x + 7 ) x + 9}{x ^{2} + 9 x}

What is the extreme ((12x^3))/3+38x^2+56x,-8<= x<= 1 ?
The extreme ((12x^3))/3+38x^2+56x,-8<= x<= 1 is