What is the extreme f(x)=(-2)/3 x^3-6x^2-10x+80 ?

The extreme f(x)=(-2)/3 x^3-6x^2-10x+80 is Minimum(-5, 190/3),Maximum(-1, 254/3)

extreme f(x)=(-2)/3 x^3-6x^2-10x+80

extreme points

f (x) = \frac{- 2}{3} x^{3} - 6 x^{2} - 10 x + 80

Minimum (- 5, \frac{190}{3}), Maximum (- 1, \frac{254}{3})

Solution steps

f^{'} (x) = - 2 x^{2} - 12 x - 10

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < - 1,

Decreasing

: - 1 < x < \infty

Plug

x = - 5

into

\frac{- 2}{3} x^{3} - 6 x^{2} - 10 x + 80 : \frac{190}{3}

Minimum (- 5, \frac{190}{3})

Plug

x = - 1

into

\frac{- 2}{3} x^{3} - 6 x^{2} - 10 x + 80 : \frac{254}{3}

Maximum (- 1, \frac{254}{3})

Minimum (- 5, \frac{190}{3}), Maximum (- 1, \frac{254}{3})

\frac{4 x + 5}{x - 7}

g (θ) = 4 θ - 7 sin (θ), 0 \leq θ \leq π

x^{2} + 14 x + 46.2

f (x) = x + ln (x^{2} - 1)

f (x) = 2 x^{3} - 33 x^{2} + 168 x + 7

What is the extreme f(x)=(-2)/3 x^3-6x^2-10x+80 ?
The extreme f(x)=(-2)/3 x^3-6x^2-10x+80 is Minimum(-5, 190/3),Maximum(-1, 254/3)