What is the extreme f(x)= 7/12 x^3+7x^2+21x+9 ?

The extreme f(x)= 7/12 x^3+7x^2+21x+9 is Maximum(-6,9),Minimum(-2,-29/3)

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extreme f(x)= 7/12 x^3+7x^2+21x+9

extreme points

f (x) = \frac{7}{12} x^{3} + 7 x^{2} + 21 x + 9

Maximum (- 6, 9), Minimum (- 2, - \frac{29}{3})

Solution steps

f^{'} (x) = \frac{7 x ^{2}}{4} + 14 x + 21

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < - 2,

Increasing

: - 2 < x < \infty

Plug

x = - 6

into

\frac{7}{12} x^{3} + 7 x^{2} + 21 x + 9 : 9

Maximum (- 6, 9)

Plug

x = - 2

into

\frac{7}{12} x^{3} + 7 x^{2} + 21 x + 9 : - \frac{29}{3}

Minimum (- 2, - \frac{29}{3})

Maximum (- 6, 9), Minimum (- 2, - \frac{29}{3})

R (x, y) = - 5 x^{2} - 4 y^{2} - 4 x y + 68 x + 72 y

f (x, y) = 9 - x^{2} - 2 y^{2}

y = x^{2} - 6 x + 5

\frac{d}{d t} (- 4.9 t^{2} + x + 21)

y = x^{2} + 2 x - 2

What is the extreme f(x)= 7/12 x^3+7x^2+21x+9 ?
The extreme f(x)= 7/12 x^3+7x^2+21x+9 is Maximum(-6,9),Minimum(-2,-29/3)