What is the extreme f(x)= 2/3 x^3+14x^2+96x+7 ?

The extreme f(x)= 2/3 x^3+14x^2+96x+7 is Maximum(-8,-619/3),Minimum(-6,-209)

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extreme f(x)= 2/3 x^3+14x^2+96x+7

extreme points

f (x) = \frac{2}{3} x^{3} + 14 x^{2} + 96 x + 7

Maximum (- 8, - \frac{619}{3}), Minimum (- 6, - 209)

Solution steps

f^{'} (x) = 2 x^{2} + 28 x + 96

Find intervals:

Increasing

: - \infty < x < - 8,

Decreasing

: - 8 < x < - 6,

Increasing

: - 6 < x < \infty

Plug

x = - 8

into

\frac{2}{3} x^{3} + 14 x^{2} + 96 x + 7 : - \frac{619}{3}

Maximum (- 8, - \frac{619}{3})

Plug

x = - 6

into

\frac{2}{3} x^{3} + 14 x^{2} + 96 x + 7 : - 209

Minimum (- 6, - 209)

Maximum (- 8, - \frac{619}{3}), Minimum (- 6, - 209)

f (x, y) = 3 x^{2} + y^{2}

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

3 x^{2} + y^{2} - x y - 11 x

x^{2} - 8 x

f (x) = - x^{3} - 6 x^{2} - 9 x + 3

What is the extreme f(x)= 2/3 x^3+14x^2+96x+7 ?
The extreme f(x)= 2/3 x^3+14x^2+96x+7 is Maximum(-8,-619/3),Minimum(-6,-209)