What is the extreme f(x)=x^3-7x^2+2 ?

The extreme f(x)=x^3-7x^2+2 is Maximum(0,2),Minimum(14/3 ,-1318/27)

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extreme f(x)=x^3-7x^2+2

extreme points

f (x) = x^{3} - 7 x^{2} + 2

Maximum (0, 2), Minimum (\frac{14}{3}, - \frac{1318}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{14}{3},

Increasing

: \frac{14}{3} < x < \infty

Plug

x = 0

into

x^{3} - 7 x^{2} + 2 : 2

Maximum (0, 2)

Plug

x = \frac{14}{3}

into

x^{3} - 7 x^{2} + 2 : - \frac{1318}{27}

Minimum (\frac{14}{3}, - \frac{1318}{27})

Maximum (0, 2), Minimum (\frac{14}{3}, - \frac{1318}{27})

What is the extreme f(x)=x^3-7x^2+2 ?
The extreme f(x)=x^3-7x^2+2 is Maximum(0,2),Minimum(14/3 ,-1318/27)