What is the extreme f(x)=-10/3 x^3-19x^2-24x+50 ?

The extreme f(x)=-10/3 x^3-19x^2-24x+50 is Minimum(-3,41),Maximum(-4/5 , 4406/75)

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extreme f(x)=-10/3 x^3-19x^2-24x+50

extreme points

f (x) = - \frac{10}{3} x^{3} - 19 x^{2} - 24 x + 50

Minimum (- 3, 41), Maximum (- \frac{4}{5}, \frac{4406}{75})

Solution steps

f^{'} (x) = - 10 x^{2} - 38 x - 24

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < - \frac{4}{5},

Decreasing

: - \frac{4}{5} < x < \infty

Plug

x = - 3

into

- \frac{10}{3} x^{3} - 19 x^{2} - 24 x + 50 : 41

Minimum (- 3, 41)

Plug

x = - \frac{4}{5}

into

- \frac{10}{3} x^{3} - 19 x^{2} - 24 x + 50 : \frac{4406}{75}

Maximum (- \frac{4}{5}, \frac{4406}{75})

Minimum (- 3, 41), Maximum (- \frac{4}{5}, \frac{4406}{75})

What is the extreme f(x)=-10/3 x^3-19x^2-24x+50 ?
The extreme f(x)=-10/3 x^3-19x^2-24x+50 is Minimum(-3,41),Maximum(-4/5 , 4406/75)