What is the extreme f(x)=x^3-2x^2+14 ?

The extreme f(x)=x^3-2x^2+14 is Maximum(0,14),Minimum(4/3 , 346/27)

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extreme f(x)=x^3-2x^2+14

extreme points

f (x) = x^{3} - 2 x^{2} + 14

Maximum (0, 14), Minimum (\frac{4}{3}, \frac{346}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{4}{3},

Increasing

: \frac{4}{3} < x < \infty

Plug

x = 0

into

x^{3} - 2 x^{2} + 14 : 14

Maximum (0, 14)

Plug

x = \frac{4}{3}

into

x^{3} - 2 x^{2} + 14 : \frac{346}{27}

Minimum (\frac{4}{3}, \frac{346}{27})

Maximum (0, 14), Minimum (\frac{4}{3}, \frac{346}{27})

f (x) = x^{3} - 2 x^{2} + 10

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

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

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

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

What is the extreme f(x)=x^3-2x^2+14 ?
The extreme f(x)=x^3-2x^2+14 is Maximum(0,14),Minimum(4/3 , 346/27)