What is the extreme f(x)=2x^3-21x^2+72x-72.5 ?

The extreme f(x)=2x^3-21x^2+72x-72.5 is Maximum(3,8.5),Minimum(4,7.5)

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extreme f(x)=2x^3-21x^2+72x-72.5

extreme points

f (x) = 2 x^{3} - 21 x^{2} + 72 x - 72.5

Maximum (3, 8.5), Minimum (4, 7.5)

Solution steps

f^{'} (x) = 6 x^{2} - 42 x + 72

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 3

into

2 x^{3} - 21 x^{2} + 72 x - 72.5 : 8.5

Maximum (3, 8.5)

Plug

x = 4

into

2 x^{3} - 21 x^{2} + 72 x - 72.5 : 7.5

Minimum (4, 7.5)

Maximum (3, 8.5), Minimum (4, 7.5)

f (x, y) = (x + 1)^{2} + x^{2} y^{2}

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

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

x + \frac{25}{x}

f (x) = 2 x^{3} - 3 x + 10

What is the extreme f(x)=2x^3-21x^2+72x-72.5 ?
The extreme f(x)=2x^3-21x^2+72x-72.5 is Maximum(3,8.5),Minimum(4,7.5)