What is the extreme f(x)=2x^3-15x^2-30 ?

The extreme f(x)=2x^3-15x^2-30 is Maximum(0,-30),Minimum(5,-155)

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extreme f(x)=2x^3-15x^2-30

extreme points

f (x) = 2 x^{3} - 15 x^{2} - 30

Maximum (0, - 30), Minimum (5, - 155)

Solution steps

f^{'} (x) = 6 x^{2} - 30 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 0

into

2 x^{3} - 15 x^{2} - 30 : - 30

Maximum (0, - 30)

Plug

x = 5

into

2 x^{3} - 15 x^{2} - 30 : - 155

Minimum (5, - 155)

Maximum (0, - 30), Minimum (5, - 155)

f (x) = 15 x^{2} - 15 x^{4}

6 x^{3} - 9 x^{2} - 216 x + 9

f (x) = \frac{x ^{4}}{4} + \frac{5}{3} x^{3} - 5 x^{2} - 50 x + 1

f (x, y) = \frac{1}{2} x^{2} + y^{3} - x y

f (x) = 2 x^{2} - 8 x + 2 (0.5)

What is the extreme f(x)=2x^3-15x^2-30 ?
The extreme f(x)=2x^3-15x^2-30 is Maximum(0,-30),Minimum(5,-155)