What is the extreme f(x)=-4x^3-6x^2+144x-11 ?

The extreme f(x)=-4x^3-6x^2+144x-11 is Minimum(-4,-427),Maximum(3,259)

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extreme f(x)=-4x^3-6x^2+144x-11

extreme points

f (x) = - 4 x^{3} - 6 x^{2} + 144 x - 11

Minimum (- 4, - 427), Maximum (3, 259)

Solution steps

f^{'} (x) = - 12 x^{2} - 12 x + 144

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 4

into

- 4 x^{3} - 6 x^{2} + 144 x - 11 : - 427

Minimum (- 4, - 427)

Plug

x = 3

into

- 4 x^{3} - 6 x^{2} + 144 x - 11 : 259

Maximum (3, 259)

Minimum (- 4, - 427), Maximum (3, 259)

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

y = 43 x + 8 cos (x), 0 \leq x \leq 2 π

f (x) = x^{3} - 6 x^{2} - 63 x + 7, - 4 \leq x \leq 8

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

f (x, y) = 4 x^{2} + 3 x y + 5 y^{2} + 5 y + 3 y

What is the extreme f(x)=-4x^3-6x^2+144x-11 ?
The extreme f(x)=-4x^3-6x^2+144x-11 is Minimum(-4,-427),Maximum(3,259)