What is the extreme f(x)=9x^3+21x^2+8x-3 ?

The extreme f(x)=9x^3+21x^2+8x-3 is Maximum(-4/3 , 7/3),Minimum(-2/9 ,-311/81)

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extreme f(x)=9x^3+21x^2+8x-3

extreme

Maximum (- \frac{4}{3}, \frac{7}{3}), Minimum (- \frac{2}{9}, - \frac{311}{81})

Solution steps

f^{'} (x) = 27 x^{2} + 42 x + 8

Find intervals:

Increasing

: - \infty < x < - \frac{4}{3},

Decreasing

: - \frac{4}{3} < x < - \frac{2}{9},

Increasing

: - \frac{2}{9} < x < \infty

Plug

x = - \frac{4}{3}

into

9 x^{3} + 21 x^{2} + 8 x - 3 : \frac{7}{3}

Maximum (- \frac{4}{3}, \frac{7}{3})

Plug

x = - \frac{2}{9}

into

9 x^{3} + 21 x^{2} + 8 x - 3 : - \frac{311}{81}

Minimum (- \frac{2}{9}, - \frac{311}{81})

Maximum (- \frac{4}{3}, \frac{7}{3}), Minimum (- \frac{2}{9}, - \frac{311}{81})

What is the extreme f(x)=9x^3+21x^2+8x-3 ?
The extreme f(x)=9x^3+21x^2+8x-3 is Maximum(-4/3 , 7/3),Minimum(-2/9 ,-311/81)