What is the extreme f(x)=-5/12 x^3-5x^2-15x-6 ?

The extreme f(x)=-5/12 x^3-5x^2-15x-6 is Minimum(-6,-6),Maximum(-2, 22/3)

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extreme f(x)=-5/12 x^3-5x^2-15x-6

extreme points

f (x) = - \frac{5}{12} x^{3} - 5 x^{2} - 15 x - 6

Minimum (- 6, - 6), Maximum (- 2, \frac{22}{3})

Solution steps

f^{'} (x) = - \frac{5 x ^{2}}{4} - 10 x - 15

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < - 2,

Decreasing

: - 2 < x < \infty

Plug

x = - 6

into

- \frac{5}{12} x^{3} - 5 x^{2} - 15 x - 6 : - 6

Minimum (- 6, - 6)

Plug

x = - 2

into

- \frac{5}{12} x^{3} - 5 x^{2} - 15 x - 6 : \frac{22}{3}

Maximum (- 2, \frac{22}{3})

Minimum (- 6, - 6), Maximum (- 2, \frac{22}{3})

y = \frac{x ^{3} + 8}{x}

f (x) = 2 x^{3} + 21 x^{2} + 72 x - 2

f (x) = 4 cos (3 x)

ln (e^{\frac{u + v}{2}}) - v

f (x) = 6 x^{2} - 6 x - 72

What is the extreme f(x)=-5/12 x^3-5x^2-15x-6 ?
The extreme f(x)=-5/12 x^3-5x^2-15x-6 is Minimum(-6,-6),Maximum(-2, 22/3)