What is the extreme-2x^3+30x^2-144x+3 ?

The extreme-2x^3+30x^2-144x+3 is Minimum(4,-221),Maximum(6,-213)

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extreme-2x^3+30x^2-144x+3

extreme points

- 2 x^{3} + 30 x^{2} - 144 x + 3

Minimum (4, - 221), Maximum (6, - 213)

Solution steps

f^{'} (x) = - 6 x^{2} + 60 x - 144

Find intervals:

Decreasing

: - \infty < x < 4,

Increasing

: 4 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 4

into

- 2 x^{3} + 30 x^{2} - 144 x + 3 : - 221

Minimum (4, - 221)

Plug

x = 6

into

- 2 x^{3} + 30 x^{2} - 144 x + 3 : - 213

Maximum (6, - 213)

Minimum (4, - 221), Maximum (6, - 213)

(2, 2), (2, - 2)

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

f (x) = - \frac{5}{3} x - 8

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

f (x) = \frac{2 x - 7}{3 x}

What is the extreme-2x^3+30x^2-144x+3 ?
The extreme-2x^3+30x^2-144x+3 is Minimum(4,-221),Maximum(6,-213)