What is the extreme-10x^4+4x^2-6 ?

The extreme-10x^4+4x^2-6 is Maximum(-1/(sqrt(5)),-28/5),Minimum(0,-6),Maximum(1/(sqrt(5)),-28/5)

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extreme-10x^4+4x^2-6

extreme

Maximum (- \frac{1}{5}, - \frac{28}{5}), Minimum (0, - 6), Maximum (\frac{1}{5}, - \frac{28}{5})

Solution steps

f^{'} (x) = - 40 x^{3} + 8 x

Find intervals:

Increasing

: - \infty < x < - \frac{1}{5},

Decreasing

: - \frac{1}{5} < x < 0,

Increasing

: 0 < x < \frac{1}{5},

Decreasing

: \frac{1}{5} < x < \infty

Plug

x = - \frac{1}{5}

into

- 10 x^{4} + 4 x^{2} - 6 : - \frac{28}{5}

Maximum (- \frac{1}{5}, - \frac{28}{5})

Plug

x = 0

into

- 10 x^{4} + 4 x^{2} - 6 : - 6

Minimum (0, - 6)

Plug

x = \frac{1}{5}

into

- 10 x^{4} + 4 x^{2} - 6 : - \frac{28}{5}

Maximum (\frac{1}{5}, - \frac{28}{5})

Maximum (- \frac{1}{5}, - \frac{28}{5}), Minimum (0, - 6), Maximum (\frac{1}{5}, - \frac{28}{5})

What is the extreme-10x^4+4x^2-6 ?
The extreme-10x^4+4x^2-6 is Maximum(-1/(sqrt(5)),-28/5),Minimum(0,-6),Maximum(1/(sqrt(5)),-28/5)