What is the extreme f(x)=x^3-9/2 x^2+1 ?

The extreme f(x)=x^3-9/2 x^2+1 is Maximum(0,1),Minimum(3,-25/2)

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extreme f(x)=x^3-9/2 x^2+1

extreme points

f (x) = x^{3} - \frac{9}{2} x^{2} + 1

Maximum (0, 1), Minimum (3, - \frac{25}{2})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

x^{3} - \frac{9}{2} x^{2} + 1 : 1

Maximum (0, 1)

Plug

x = 3

into

x^{3} - \frac{9}{2} x^{2} + 1 : - \frac{25}{2}

Minimum (3, - \frac{25}{2})

Maximum (0, 1), Minimum (3, - \frac{25}{2})

y = 2 x^{2} + z^{2}

f (x, y) = 1 - 3 x^{4} - 6 x^{2} y + 2 y^{3}

f (x) = 8 x^{3} + 13 x

f (x, y) = 18 y^{2} + x^{2} - x^{2} y

2 (\frac{1}{2})^{x}

What is the extreme f(x)=x^3-9/2 x^2+1 ?
The extreme f(x)=x^3-9/2 x^2+1 is Maximum(0,1),Minimum(3,-25/2)