What is the extreme f(x)=(10x^3)/3-(11x^2)/2+x+2 ?

The extreme f(x)=(10x^3)/3-(11x^2)/2+x+2 is Maximum(1/10 , 1229/600),Minimum(1, 5/6)

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extreme f(x)=(10x^3)/3-(11x^2)/2+x+2

extreme

Maximum (\frac{1}{10}, \frac{1229}{600}), Minimum (1, \frac{5}{6})

Solution steps

f^{'} (x) = 10 x^{2} - 11 x + 1

Find intervals:

Increasing

: - \infty < x < \frac{1}{10},

Decreasing

: \frac{1}{10} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = \frac{1}{10}

into

\frac{10 x ^{3}}{3} - \frac{11 x ^{2}}{2} + x + 2 : \frac{1229}{600}

Maximum (\frac{1}{10}, \frac{1229}{600})

Plug

x = 1

into

\frac{10 x ^{3}}{3} - \frac{11 x ^{2}}{2} + x + 2 : \frac{5}{6}

Minimum (1, \frac{5}{6})

Maximum (\frac{1}{10}, \frac{1229}{600}), Minimum (1, \frac{5}{6})

What is the extreme f(x)=(10x^3)/3-(11x^2)/2+x+2 ?
The extreme f(x)=(10x^3)/3-(11x^2)/2+x+2 is Maximum(1/10 , 1229/600),Minimum(1, 5/6)