What is the extreme f(x)=-2/3 x^3-11/2 x^2-5x+9 ?

The extreme f(x)=-2/3 x^3-11/2 x^2-5x+9 is Minimum(-5,-121/6),Maximum(-1/2 , 245/24)

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extreme f(x)=-2/3 x^3-11/2 x^2-5x+9

extreme

Minimum (- 5, - \frac{121}{6}), Maximum (- \frac{1}{2}, \frac{245}{24})

Solution steps

f^{'} (x) = - 2 x^{2} - 11 x - 5

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < \infty

Plug

x = - 5

into

- \frac{2}{3} x^{3} - \frac{11}{2} x^{2} - 5 x + 9 : - \frac{121}{6}

Minimum (- 5, - \frac{121}{6})

Plug

x = - \frac{1}{2}

into

- \frac{2}{3} x^{3} - \frac{11}{2} x^{2} - 5 x + 9 : \frac{245}{24}

Maximum (- \frac{1}{2}, \frac{245}{24})

Minimum (- 5, - \frac{121}{6}), Maximum (- \frac{1}{2}, \frac{245}{24})

What is the extreme f(x)=-2/3 x^3-11/2 x^2-5x+9 ?
The extreme f(x)=-2/3 x^3-11/2 x^2-5x+9 is Minimum(-5,-121/6),Maximum(-1/2 , 245/24)