What is the extreme f(x)=4x^3-18x^2+24x ?

The extreme f(x)=4x^3-18x^2+24x is Maximum(1,10),Minimum(2,8)

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extreme f(x)=4x^3-18x^2+24x

extreme points

f (x) = 4 x^{3} - 18 x^{2} + 24 x

Maximum (1, 10), Minimum (2, 8)

Solution steps

f^{'} (x) = 12 x^{2} - 36 x + 24

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 1

into

4 x^{3} - 18 x^{2} + 24 x : 10

Maximum (1, 10)

Plug

x = 2

into

4 x^{3} - 18 x^{2} + 24 x : 8

Minimum (2, 8)

Maximum (1, 10), Minimum (2, 8)

f (x) = \frac{1}{x ^{2} + 10 x + 28}

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

8 x + 3

- x + 2

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

What is the extreme f(x)=4x^3-18x^2+24x ?
The extreme f(x)=4x^3-18x^2+24x is Maximum(1,10),Minimum(2,8)