What is the extreme f(x)=-1/3 x^3+2x^2+12x+28 ?

The extreme f(x)=-1/3 x^3+2x^2+12x+28 is Minimum(-2, 44/3),Maximum(6,100)

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extreme f(x)=-1/3 x^3+2x^2+12x+28

extreme points

f (x) = - \frac{1}{3} x^{3} + 2 x^{2} + 12 x + 28

Minimum (- 2, \frac{44}{3}), Maximum (6, 100)

Solution steps

f^{'} (x) = - x^{2} + 4 x + 12

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = - 2

into

- \frac{1}{3} x^{3} + 2 x^{2} + 12 x + 28 : \frac{44}{3}

Minimum (- 2, \frac{44}{3})

Plug

x = 6

into

- \frac{1}{3} x^{3} + 2 x^{2} + 12 x + 28 : 100

Maximum (6, 100)

Minimum (- 2, \frac{44}{3}), Maximum (6, 100)

f (x) = - 0.015 x^{2} + 1.22 x - 7.2

f (x) = 8 - x

f (x) = 6 + 81 x - 3 x^{3}, 0 \leq x \leq 4

f (x) = \frac{x ^{2} + 69}{x + 10}

\frac{t ^{2}}{t + 3}

What is the extreme f(x)=-1/3 x^3+2x^2+12x+28 ?
The extreme f(x)=-1/3 x^3+2x^2+12x+28 is Minimum(-2, 44/3),Maximum(6,100)