What is the extreme f(x)=2x^3-6x^2-48x ?

The extreme f(x)=2x^3-6x^2-48x is Maximum(-2,56),Minimum(4,-160)

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extreme f(x)=2x^3-6x^2-48x

extreme points

f (x) = 2 x^{3} - 6 x^{2} - 48 x

Maximum (- 2, 56), Minimum (4, - 160)

Solution steps

f^{'} (x) = 6 x^{2} - 12 x - 48

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 2

into

2 x^{3} - 6 x^{2} - 48 x : 56

Maximum (- 2, 56)

Plug

x = 4

into

2 x^{3} - 6 x^{2} - 48 x : - 160

Minimum (4, - 160)

Maximum (- 2, 56), Minimum (4, - 160)

f (x) = x^{2} - 6 x y + y^{2} + 16 y + 9

y = 3 x^{3} e^{- x}

f (a, b) = (9 a^{2} + 3 b^{2}) e^{(ab)^{2}}

- (x - 10) (x - 60)

f (x) = x^{4} - 24 x^{2} = x^{2} (x^{2} - 24)

What is the extreme f(x)=2x^3-6x^2-48x ?
The extreme f(x)=2x^3-6x^2-48x is Maximum(-2,56),Minimum(4,-160)