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

The extreme f(x)= 1/4 x^4+2/3 x^3-3/2 x^2+4 is Minimum(-3,-29/4),Maximum(0,4),Minimum(1, 41/12)

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

extreme points

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

Minimum (- 3, - \frac{29}{4}), Maximum (0, 4), Minimum (1, \frac{41}{12})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 3

into

\frac{1}{4} x^{4} + \frac{2}{3} x^{3} - \frac{3}{2} x^{2} + 4 : - \frac{29}{4}

Minimum (- 3, - \frac{29}{4})

Plug

x = 0

into

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

Maximum (0, 4)

Plug

x = 1

into

\frac{1}{4} x^{4} + \frac{2}{3} x^{3} - \frac{3}{2} x^{2} + 4 : \frac{41}{12}

Minimum (1, \frac{41}{12})

Minimum (- 3, - \frac{29}{4}), Maximum (0, 4), Minimum (1, \frac{41}{12})

f (x) = x y^{2} = 9

f (x) = sin (θ)

f (x, y) = x^{2} + 4 y^{2} - 2 ln (x y)

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

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

What is the extreme f(x)= 1/4 x^4+2/3 x^3-3/2 x^2+4 ?
The extreme f(x)= 1/4 x^4+2/3 x^3-3/2 x^2+4 is Minimum(-3,-29/4),Maximum(0,4),Minimum(1, 41/12)