What is the extreme f(x)=-3x^4+30x^2-27 ?

The extreme f(x)=-3x^4+30x^2-27 is Maximum(-sqrt(5),48),Minimum(0,-27),Maximum(sqrt(5),48)

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extreme f(x)=-3x^4+30x^2-27

extreme points

f (x) = - 3 x^{4} + 30 x^{2} - 27

Maximum (- 5, 48), Minimum (0, - 27), Maximum (5, 48)

Solution steps

f^{'} (x) = - 12 x^{3} + 60 x

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 0,

Increasing

: 0 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 5

into

- 3 x^{4} + 30 x^{2} - 27 : 48

Maximum (- 5, 48)

Plug

x = 0

into

- 3 x^{4} + 30 x^{2} - 27 : - 27

Minimum (0, - 27)

Plug

x = 5

into

- 3 x^{4} + 30 x^{2} - 27 : 48

Maximum (5, 48)

Maximum (- 5, 48), Minimum (0, - 27), Maximum (5, 48)

f (x) = \frac{4}{2 x - 1}

y - x = 5

x - 5 = 0

g (x) = x^{3} - 2

y = 0.6 x + 3, (- 3, - 5)

What is the extreme f(x)=-3x^4+30x^2-27 ?
The extreme f(x)=-3x^4+30x^2-27 is Maximum(-sqrt(5),48),Minimum(0,-27),Maximum(sqrt(5),48)