What is the extreme f(x)=-1/2 x^4+2x^3+40x^2-13 ?

The extreme f(x)=-1/2 x^4+2x^3+40x^2-13 is Maximum(-5, 849/2),Minimum(0,-13),Maximum(8,1523)

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extreme f(x)=-1/2 x^4+2x^3+40x^2-13

extreme points

f (x) = - \frac{1}{2} x^{4} + 2 x^{3} + 40 x^{2} - 13

Maximum (- 5, \frac{849}{2}), Minimum (0, - 13), Maximum (8, 1523)

Solution steps

f^{'} (x) = - 2 x^{3} + 6 x^{2} + 80 x

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 0,

Increasing

: 0 < x < 8,

Decreasing

: 8 < x < \infty

Plug

x = - 5

into

- \frac{1}{2} x^{4} + 2 x^{3} + 40 x^{2} - 13 : \frac{849}{2}

Maximum (- 5, \frac{849}{2})

Plug

x = 0

into

- \frac{1}{2} x^{4} + 2 x^{3} + 40 x^{2} - 13 : - 13

Minimum (0, - 13)

Plug

x = 8

into

- \frac{1}{2} x^{4} + 2 x^{3} + 40 x^{2} - 13 : 1523

Maximum (8, 1523)

Maximum (- 5, \frac{849}{2}), Minimum (0, - 13), Maximum (8, 1523)

f (x) = 3 x - 2 x^{2} - \frac{4}{3} x^{3}

f (x) = (x^{3} - 5 x^{2} + 11 x - 11) e^{x}

f (x) = x^{2} + y^{2} + \frac{2}{x y}

f (x, y) = - 14 + 5 \cdot x^{2} + x \cdot y + y^{2}

f (x) = 5 x + \frac{3}{x}

What is the extreme f(x)=-1/2 x^4+2x^3+40x^2-13 ?
The extreme f(x)=-1/2 x^4+2x^3+40x^2-13 is Maximum(-5, 849/2),Minimum(0,-13),Maximum(8,1523)