What is the extreme f(x)=4x^3-2x^2-5 ?

The extreme f(x)=4x^3-2x^2-5 is Maximum(0,-5),Minimum(1/3 ,-137/27)

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extreme f(x)=4x^3-2x^2-5

extreme points

f (x) = 4 x^{3} - 2 x^{2} - 5

Maximum (0, - 5), Minimum (\frac{1}{3}, - \frac{137}{27})

Solution steps

f^{'} (x) = 12 x^{2} - 4 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = 0

into

4 x^{3} - 2 x^{2} - 5 : - 5

Maximum (0, - 5)

Plug

x = \frac{1}{3}

into

4 x^{3} - 2 x^{2} - 5 : - \frac{137}{27}

Minimum (\frac{1}{3}, - \frac{137}{27})

Maximum (0, - 5), Minimum (\frac{1}{3}, - \frac{137}{27})

T (x, y) = ln (3 x y + 2 x^{2} - y)

f (x) = 5000 - 15 x + 0.08 x^{2}

2 y^{2} + 2 x y + x^{2} - 16 x - 20 y

f (x) = - 2 x^{2} + 200 x

y = x^{2} - 5 x - 14

What is the extreme f(x)=4x^3-2x^2-5 ?
The extreme f(x)=4x^3-2x^2-5 is Maximum(0,-5),Minimum(1/3 ,-137/27)