What is the extreme f(x)=5+6x-8x^3 ?

The extreme f(x)=5+6x-8x^3 is Minimum(-1/2 ,3),Maximum(1/2 ,7)

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extreme f(x)=5+6x-8x^3

extreme points

f (x) = 5 + 6 x - 8 x^{3}

Minimum (- \frac{1}{2}, 3), Maximum (\frac{1}{2}, 7)

Solution steps

f^{'} (x) = - 24 x^{2} + 6

Find intervals:

Decreasing

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

Increasing

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

Decreasing

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

Plug

x = - \frac{1}{2}

into

5 + 6 x - 8 x^{3} : 3

Minimum (- \frac{1}{2}, 3)

Plug

x = \frac{1}{2}

into

5 + 6 x - 8 x^{3} : 7

Maximum (\frac{1}{2}, 7)

Minimum (- \frac{1}{2}, 3), Maximum (\frac{1}{2}, 7)

f (x) = 2 x^{3} + 24 x + 5

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

f (x, y) = x y + y x

f (x) = x^{2} - 8 ln (x)

P (x, y) = (x + 1)^{2} - (y - 2)^{2}

What is the extreme f(x)=5+6x-8x^3 ?
The extreme f(x)=5+6x-8x^3 is Minimum(-1/2 ,3),Maximum(1/2 ,7)