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})

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

3 t (8 - t)

f (x) = - x^{2} + 50 ln (x)

f (x) = - 69.7 x^{2} + 625.6 x

f (x) = \frac{1}{2} (x + 4)^{2} + 6

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)