What is the extreme-x^3+2x^2+4x+7 ?

The extreme-x^3+2x^2+4x+7 is Minimum(-2/3 , 149/27),Maximum(2,15)

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extreme-x^3+2x^2+4x+7

extreme points

- x^{3} + 2 x^{2} + 4 x + 7

Minimum (- \frac{2}{3}, \frac{149}{27}), Maximum (2, 15)

Solution steps

f^{'} (x) = - 3 x^{2} + 4 x + 4

Find intervals:

Decreasing

: - \infty < x < - \frac{2}{3},

Increasing

: - \frac{2}{3} < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - \frac{2}{3}

into

- x^{3} + 2 x^{2} + 4 x + 7 : \frac{149}{27}

Minimum (- \frac{2}{3}, \frac{149}{27})

Plug

x = 2

into

- x^{3} + 2 x^{2} + 4 x + 7 : 15

Maximum (2, 15)

Minimum (- \frac{2}{3}, \frac{149}{27}), Maximum (2, 15)

f (x) = 2 x^{3} - 39 x^{2} + 180 x + 1

y = 6 x - 12

1353.0186700000000 \dots

f (x) = \frac{1}{8} (x + 4)^{2} (6 - x)

f (x) = ln (\frac{4 x ^{2}}{ln ( x )})

What is the extreme-x^3+2x^2+4x+7 ?
The extreme-x^3+2x^2+4x+7 is Minimum(-2/3 , 149/27),Maximum(2,15)