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

The extreme f(x)= 3/2 x^4-x^6 is Maximum(-1, 1/2),Minimum(0,0),Maximum(1, 1/2)

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extreme f(x)= 3/2 x^4-x^6

extreme points

f (x) = \frac{3}{2} x^{4} - x^{6}

Maximum (- 1, \frac{1}{2}), Minimum (0, 0), Maximum (1, \frac{1}{2})

Solution steps

f^{'} (x) = 6 x^{3} - 6 x^{5}

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

\frac{3}{2} x^{4} - x^{6} : \frac{1}{2}

Maximum (- 1, \frac{1}{2})

Plug

x = 0

into

\frac{3}{2} x^{4} - x^{6} : 0

Minimum (0, 0)

Plug

x = 1

into

\frac{3}{2} x^{4} - x^{6} : \frac{1}{2}

Maximum (1, \frac{1}{2})

Maximum (- 1, \frac{1}{2}), Minimum (0, 0), Maximum (1, \frac{1}{2})

f (x, y) = - 3 x^{2} + 7 x y - 4 y^{2} + x + y

x^{4} + x^{3} - 6 x^{2}

f (x) = x^{3} - 27 x + 7

f (x) = 2 x^{3} - 9 x^{2} + 7 x + 6

f (x) = \frac{x - 5}{x ^{2}}

What is the extreme f(x)= 3/2 x^4-x^6 ?
The extreme f(x)= 3/2 x^4-x^6 is Maximum(-1, 1/2),Minimum(0,0),Maximum(1, 1/2)