What is the extreme f(x)=(-2)/3 x^3+9x^2-28x+1 ?

The extreme f(x)=(-2)/3 x^3+9x^2-28x+1 is Minimum(2,-73/3),Maximum(7, 52/3)

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extreme f(x)=(-2)/3 x^3+9x^2-28x+1

extreme

Minimum (2, - \frac{73}{3}), Maximum (7, \frac{52}{3})

Solution steps

f^{'} (x) = - 2 x^{2} + 18 x - 28

Find intervals:

Decreasing

: - \infty < x < 2,

Increasing

: 2 < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = 2

into

\frac{- 2}{3} x^{3} + 9 x^{2} - 28 x + 1 : - \frac{73}{3}

Minimum (2, - \frac{73}{3})

Plug

x = 7

into

\frac{- 2}{3} x^{3} + 9 x^{2} - 28 x + 1 : \frac{52}{3}

Maximum (7, \frac{52}{3})

Minimum (2, - \frac{73}{3}), Maximum (7, \frac{52}{3})

What is the extreme f(x)=(-2)/3 x^3+9x^2-28x+1 ?
The extreme f(x)=(-2)/3 x^3+9x^2-28x+1 is Minimum(2,-73/3),Maximum(7, 52/3)