What is the extreme f(x)=15x^2-15x^4 ?

The extreme f(x)=15x^2-15x^4 is Maximum(-1/(sqrt(2)), 15/4),Minimum(0,0),Maximum(1/(sqrt(2)), 15/4)

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extreme f(x)=15x^2-15x^4

extreme points

f (x) = 15 x^{2} - 15 x^{4}

Maximum (- \frac{1}{2}, \frac{15}{4}), Minimum (0, 0), Maximum (\frac{1}{2}, \frac{15}{4})

Solution steps

f^{'} (x) = 30 x - 60 x^{3}

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < 0,

Increasing

: 0 < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

15 x^{2} - 15 x^{4} : \frac{15}{4}

Maximum (- \frac{1}{2}, \frac{15}{4})

Plug

x = 0

into

15 x^{2} - 15 x^{4} : 0

Minimum (0, 0)

Plug

x = \frac{1}{2}

into

15 x^{2} - 15 x^{4} : \frac{15}{4}

Maximum (\frac{1}{2}, \frac{15}{4})

Maximum (- \frac{1}{2}, \frac{15}{4}), Minimum (0, 0), Maximum (\frac{1}{2}, \frac{15}{4})

6 x^{3} - 9 x^{2} - 216 x + 9

f (x) = \frac{x ^{4}}{4} + \frac{5}{3} x^{3} - 5 x^{2} - 50 x + 1

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

f (x) = 2 x^{2} - 8 x + 2 (0.5)

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

What is the extreme f(x)=15x^2-15x^4 ?
The extreme f(x)=15x^2-15x^4 is Maximum(-1/(sqrt(2)), 15/4),Minimum(0,0),Maximum(1/(sqrt(2)), 15/4)