What is the extreme f(x)=(-7)/3 x^3+14x^2+147x+2 ?

The extreme f(x)=(-7)/3 x^3+14x^2+147x+2 is Minimum(-3,-250),Maximum(7, 2750/3)

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extreme f(x)=(-7)/3 x^3+14x^2+147x+2

extreme points

f (x) = \frac{- 7}{3} x^{3} + 14 x^{2} + 147 x + 2

Minimum (- 3, - 250), Maximum (7, \frac{2750}{3})

Solution steps

f^{'} (x) = - 7 x^{2} + 28 x + 147

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = - 3

into

\frac{- 7}{3} x^{3} + 14 x^{2} + 147 x + 2 : - 250

Minimum (- 3, - 250)

Plug

x = 7

into

\frac{- 7}{3} x^{3} + 14 x^{2} + 147 x + 2 : \frac{2750}{3}

Maximum (7, \frac{2750}{3})

Minimum (- 3, - 250), Maximum (7, \frac{2750}{3})

- \frac{5 x ^{3}}{3} + 10 x^{2} - 15 x

\frac{x}{( x + 2 ) ^{2}}

f (x) = (1 - 2 x)^{3}

f (x) = 3 x + 5

f (x, y) = 4 x y + y^{2}

What is the extreme f(x)=(-7)/3 x^3+14x^2+147x+2 ?
The extreme f(x)=(-7)/3 x^3+14x^2+147x+2 is Minimum(-3,-250),Maximum(7, 2750/3)