What is the extreme f(x)=2x^3-24x^2+72x+5 ?

The extreme f(x)=2x^3-24x^2+72x+5 is Maximum(2,69),Minimum(6,5)

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extreme f(x)=2x^3-24x^2+72x+5

extreme points

f (x) = 2 x^{3} - 24 x^{2} + 72 x + 5

Maximum (2, 69), Minimum (6, 5)

Solution steps

f^{'} (x) = 6 x^{2} - 48 x + 72

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 2

into

2 x^{3} - 24 x^{2} + 72 x + 5 : 69

Maximum (2, 69)

Plug

x = 6

into

2 x^{3} - 24 x^{2} + 72 x + 5 : 5

Minimum (6, 5)

Maximum (2, 69), Minimum (6, 5)

f (x) = 2 + 54 x - 2 x^{3}

f (x, y) = 4 + 2 x - 4 y - x^{2} - y^{2}

f (x, y) = - 2 x^{2} - 2 y^{2} - 4 x y + 5 x + 4 y

f (x) = 2 x^{3} - 9 x^{2} - 12 x - 1

f (x) = x^{3} (x + 4)

What is the extreme f(x)=2x^3-24x^2+72x+5 ?
The extreme f(x)=2x^3-24x^2+72x+5 is Maximum(2,69),Minimum(6,5)