What is the extreme 4x^3-6x ?

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

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extreme 4x^3-6x

extreme points

4 x^{3} - 6 x

Maximum (- \frac{1}{2}, 22), Minimum (\frac{1}{2}, - 22)

Solution steps

f^{'} (x) = 12 x^{2} - 6

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{1}{2}

into

4 x^{3} - 6 x : 22

Maximum (- \frac{1}{2}, 22)

Plug

x = \frac{1}{2}

into

4 x^{3} - 6 x : - 22

Minimum (\frac{1}{2}, - 22)

Maximum (- \frac{1}{2}, 22), Minimum (\frac{1}{2}, - 22)

y \cdot ln (x) + y

5 x + 5 sin (x)

80 x - 16 x^{2}

f (x) = 19 + 4 x - x^{2}, 0 \leq x \leq 5

x^{2} + 3 x - 7

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