What is the extreme-1/2 x^3-3/2 x^2 ?

The extreme-1/2 x^3-3/2 x^2 is Minimum(-2,-2),Maximum(0,0)

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extreme-1/2 x^3-3/2 x^2

extreme points

- \frac{1}{2} x^{3} - \frac{3}{2} x^{2}

Minimum (- 2, - 2), Maximum (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 2

into

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

Minimum (- 2, - 2)

Plug

x = 0

into

- \frac{1}{2} x^{3} - \frac{3}{2} x^{2} : 0

Maximum (0, 0)

Minimum (- 2, - 2), Maximum (0, 0)

f (x, y) = \frac{sin ( x - y )}{∣ x ∣ + ∣ y ∣}

f (x) = \frac{x}{5 x - 4}, 6 \leq x \leq 7

f (x) = 4 x^{\frac{10}{3}} - 10 x^{\frac{4}{3}}

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

f (x) = 4 x^{2} - 6 x y + 5 y^{2} - 20 x + 26 y

What is the extreme-1/2 x^3-3/2 x^2 ?
The extreme-1/2 x^3-3/2 x^2 is Minimum(-2,-2),Maximum(0,0)