What is the extreme f(x)=3x^4-8x^3-6x^2+24x-3 ?

The extreme f(x)=3x^4-8x^3-6x^2+24x-3 is Minimum(-1,-22),Maximum(1,10),Minimum(2,5)

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extreme f(x)=3x^4-8x^3-6x^2+24x-3

extreme

Minimum (- 1, - 22), Maximum (1, 10), Minimum (2, 5)

Solution steps

f^{'} (x) = 12 x^{3} - 24 x^{2} - 12 x + 24

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 1

into

3 x^{4} - 8 x^{3} - 6 x^{2} + 24 x - 3 : - 22

Minimum (- 1, - 22)

Plug

x = 1

into

3 x^{4} - 8 x^{3} - 6 x^{2} + 24 x - 3 : 10

Maximum (1, 10)

Plug

x = 2

into

3 x^{4} - 8 x^{3} - 6 x^{2} + 24 x - 3 : 5

Minimum (2, 5)

Minimum (- 1, - 22), Maximum (1, 10), Minimum (2, 5)

What is the extreme f(x)=3x^4-8x^3-6x^2+24x-3 ?
The extreme f(x)=3x^4-8x^3-6x^2+24x-3 is Minimum(-1,-22),Maximum(1,10),Minimum(2,5)