What is the extreme-3x^3+5x^2+16x ?

The extreme-3x^3+5x^2+16x is Minimum(-8/9 ,-1984/243),Maximum(2,28)

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extreme-3x^3+5x^2+16x

extreme points

- 3 x^{3} + 5 x^{2} + 16 x

Minimum (- \frac{8}{9}, - \frac{1984}{243}), Maximum (2, 28)

Solution steps

f^{'} (x) = - 9 x^{2} + 10 x + 16

Find intervals:

Decreasing

: - \infty < x < - \frac{8}{9},

Increasing

: - \frac{8}{9} < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - \frac{8}{9}

into

- 3 x^{3} + 5 x^{2} + 16 x : - \frac{1984}{243}

Minimum (- \frac{8}{9}, - \frac{1984}{243})

Plug

x = 2

into

- 3 x^{3} + 5 x^{2} + 16 x : 28

Maximum (2, 28)

Minimum (- \frac{8}{9}, - \frac{1984}{243}), Maximum (2, 28)

What is the extreme-3x^3+5x^2+16x ?
The extreme-3x^3+5x^2+16x is Minimum(-8/9 ,-1984/243),Maximum(2,28)