What is the extreme f(x)= 4/3 x^3-13/2 x^2-3x+11 ?

The extreme f(x)= 4/3 x^3-13/2 x^2-3x+11 is

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extreme f(x)= 4/3 x^3-13/2 x^2-3x+11

extreme

Maximum (\frac{13 - 217}{8}, \frac{217 217 - 3133}{192} + 11), Minimum (\frac{13 + 217}{8}, \frac{- 3133 - 217 217}{192} + 11)

Solution steps

f^{'} (x) = 4 x^{2} - 13 x - 3

Find intervals:

Increasing

: - \infty < x < \frac{- 217 + 13}{8},

Decreasing

: \frac{- 217 + 13}{8} < x < \frac{217 + 13}{8},

Increasing

: \frac{217 + 13}{8} < x < \infty

Plug

x = \frac{13 - 217}{8}

into

\frac{4}{3} x^{3} - \frac{13}{2} x^{2} - 3 x + 11 : \frac{217 217 - 3133}{192} + 11

Maximum (\frac{13 - 217}{8}, \frac{217 217 - 3133}{192} + 11)

Plug

x = \frac{13 + 217}{8}

into

\frac{4}{3} x^{3} - \frac{13}{2} x^{2} - 3 x + 11 : \frac{- 3133 - 217 217}{192} + 11

Minimum (\frac{13 + 217}{8}, \frac{- 3133 - 217 217}{192} + 11)

Maximum (\frac{13 - 217}{8}, \frac{217 217 - 3133}{192} + 11), Minimum (\frac{13 + 217}{8}, \frac{- 3133 - 217 217}{192} + 11)

What is the extreme f(x)= 4/3 x^3-13/2 x^2-3x+11 ?
The extreme f(x)= 4/3 x^3-13/2 x^2-3x+11 is