What is the extreme 0.0025x^4+0.5x^3-8x^2+1000 ?

The extreme 0.0025x^4+0.5x^3-8x^2+1000 is Minimum(-160,-613400),Maximum(0,1000),Minimum(10,725)

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extreme 0.0025x^4+0.5x^3-8x^2+1000

extreme points

0.0025 x^{4} + 0.5 x^{3} - 8 x^{2} + 1000

Minimum (- 160, - 613400), Maximum (0, 1000), Minimum (10, 725)

Solution steps

f^{'} (x) = 0.01 x^{3} + 1.5 x^{2} - 16 x

Find intervals:

Decreasing

: - \infty < x < - 160,

Increasing

: - 160 < x < 0,

Decreasing

: 0 < x < 10,

Increasing

: 10 < x < \infty

Plug

x = - 160

into

0.0025 x^{4} + 0.5 x^{3} - 8 x^{2} + 1000 : - 613400

Minimum (- 160, - 613400)

Plug

x = 0

into

0.0025 x^{4} + 0.5 x^{3} - 8 x^{2} + 1000 : 1000

Maximum (0, 1000)

Plug

x = 10

into

0.0025 x^{4} + 0.5 x^{3} - 8 x^{2} + 1000 : 725

Minimum (10, 725)

Minimum (- 160, - 613400), Maximum (0, 1000), Minimum (10, 725)

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

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

f (x) = - x^{4} - 17 x^{3} - 106 x^{2} - 290 x - 293

f (x) = sin (4 x), - \frac{π}{6} \leq x \leq \frac{π}{4}

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

What is the extreme 0.0025x^4+0.5x^3-8x^2+1000 ?
The extreme 0.0025x^4+0.5x^3-8x^2+1000 is Minimum(-160,-613400),Maximum(0,1000),Minimum(10,725)