What is the extreme f(x)= 1/4 x^4-2/3 x^3-3/2 x^2+1 ?

The extreme f(x)= 1/4 x^4-2/3 x^3-3/2 x^2+1 is Minimum(-1, 5/12),Maximum(0,1),Minimum(3,-41/4)

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extreme f(x)= 1/4 x^4-2/3 x^3-3/2 x^2+1

extreme points

f (x) = \frac{1}{4} x^{4} - \frac{2}{3} x^{3} - \frac{3}{2} x^{2} + 1

Minimum (- 1, \frac{5}{12}), Maximum (0, 1), Minimum (3, - \frac{41}{4})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 1

into

\frac{1}{4} x^{4} - \frac{2}{3} x^{3} - \frac{3}{2} x^{2} + 1 : \frac{5}{12}

Minimum (- 1, \frac{5}{12})

Plug

x = 0

into

\frac{1}{4} x^{4} - \frac{2}{3} x^{3} - \frac{3}{2} x^{2} + 1 : 1

Maximum (0, 1)

Plug

x = 3

into

\frac{1}{4} x^{4} - \frac{2}{3} x^{3} - \frac{3}{2} x^{2} + 1 : - \frac{41}{4}

Minimum (3, - \frac{41}{4})

Minimum (- 1, \frac{5}{12}), Maximum (0, 1), Minimum (3, - \frac{41}{4})

f (x, y) = \frac{3 x ^{2} - 1}{x ^{2} + y ^{2} + 1}

f (x) = 3 x + \frac{27}{x}

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

f (x) = \frac{2}{3} x^{3} - 4 x^{2} - 45 x

f (x, y) = ln (x + y + 4)

What is the extreme f(x)= 1/4 x^4-2/3 x^3-3/2 x^2+1 ?
The extreme f(x)= 1/4 x^4-2/3 x^3-3/2 x^2+1 is Minimum(-1, 5/12),Maximum(0,1),Minimum(3,-41/4)