What is the extreme f(x)= 5/3 x^3+18x^2-32x-30 ?

The extreme f(x)= 5/3 x^3+18x^2-32x-30 is Maximum(-8, 1574/3),Minimum(4/5 ,-3242/75)

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extreme f(x)= 5/3 x^3+18x^2-32x-30

extreme points

f (x) = \frac{5}{3} x^{3} + 18 x^{2} - 32 x - 30

Maximum (- 8, \frac{1574}{3}), Minimum (\frac{4}{5}, - \frac{3242}{75})

Solution steps

f^{'} (x) = 5 x^{2} + 36 x - 32

Find intervals:

Increasing

: - \infty < x < - 8,

Decreasing

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

Increasing

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

Plug

x = - 8

into

\frac{5}{3} x^{3} + 18 x^{2} - 32 x - 30 : \frac{1574}{3}

Maximum (- 8, \frac{1574}{3})

Plug

x = \frac{4}{5}

into

\frac{5}{3} x^{3} + 18 x^{2} - 32 x - 30 : - \frac{3242}{75}

Minimum (\frac{4}{5}, - \frac{3242}{75})

Maximum (- 8, \frac{1574}{3}), Minimum (\frac{4}{5}, - \frac{3242}{75})

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

f (x, y) = y x - y^{2} - x + 6 y

f (x) = x^{3} - 6 x y + 8 y^{3}

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

f (x, y) = 5 x y - 7 x^{2} + 3 x - 6 y + 2

What is the extreme f(x)= 5/3 x^3+18x^2-32x-30 ?
The extreme f(x)= 5/3 x^3+18x^2-32x-30 is Maximum(-8, 1574/3),Minimum(4/5 ,-3242/75)