What is the extreme f(x)= 8/135 x^3-1/20 x^2-7/16 x ?

The extreme f(x)= 8/135 x^3-1/20 x^2-7/16 x is Maximum(-21/16 , 1813/5120),Minimum(15/8 ,-155/256)

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extreme f(x)= 8/135 x^3-1/20 x^2-7/16 x

extreme points

f (x) = \frac{8}{135} x^{3} - \frac{1}{20} x^{2} - \frac{7}{16} x

Maximum (- \frac{21}{16}, \frac{1813}{5120}), Minimum (\frac{15}{8}, - \frac{155}{256})

Solution steps

f^{'} (x) = \frac{8 x ^{2}}{45} - \frac{x}{10} - \frac{7}{16}

Find intervals:

Increasing

: - \infty < x < - \frac{21}{16},

Decreasing

: - \frac{21}{16} < x < \frac{15}{8},

Increasing

: \frac{15}{8} < x < \infty

Plug

x = - \frac{21}{16}

into

\frac{8}{135} x^{3} - \frac{1}{20} x^{2} - \frac{7}{16} x : \frac{1813}{5120}

Maximum (- \frac{21}{16}, \frac{1813}{5120})

Plug

x = \frac{15}{8}

into

\frac{8}{135} x^{3} - \frac{1}{20} x^{2} - \frac{7}{16} x : - \frac{155}{256}

Minimum (\frac{15}{8}, - \frac{155}{256})

Maximum (- \frac{21}{16}, \frac{1813}{5120}), Minimum (\frac{15}{8}, - \frac{155}{256})

What is the extreme f(x)= 8/135 x^3-1/20 x^2-7/16 x ?
The extreme f(x)= 8/135 x^3-1/20 x^2-7/16 x is Maximum(-21/16 , 1813/5120),Minimum(15/8 ,-155/256)