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

The extreme-x^3+4x^2+3x+4 is Minimum(-1/3 , 94/27),Maximum(3,22)

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

extreme points

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

Minimum (- \frac{1}{3}, \frac{94}{27}), Maximum (3, 22)

Solution steps

f^{'} (x) = - 3 x^{2} + 8 x + 3

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{3},

Increasing

: - \frac{1}{3} < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - \frac{1}{3}

into

- x^{3} + 4 x^{2} + 3 x + 4 : \frac{94}{27}

Minimum (- \frac{1}{3}, \frac{94}{27})

Plug

x = 3

into

- x^{3} + 4 x^{2} + 3 x + 4 : 22

Maximum (3, 22)

Minimum (- \frac{1}{3}, \frac{94}{27}), Maximum (3, 22)

What is the extreme-x^3+4x^2+3x+4 ?
The extreme-x^3+4x^2+3x+4 is Minimum(-1/3 , 94/27),Maximum(3,22)