What is the extreme f(x)=x^3-7x^2+15x+9 ?

The extreme f(x)=x^3-7x^2+15x+9 is Maximum(5/3 , 518/27),Minimum(3,18)

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extreme f(x)=x^3-7x^2+15x+9

extreme points

f (x) = x^{3} - 7 x^{2} + 15 x + 9

Maximum (\frac{5}{3}, \frac{518}{27}), Minimum (3, 18)

Solution steps

f^{'} (x) = 3 x^{2} - 14 x + 15

Find intervals:

Increasing

: - \infty < x < \frac{5}{3},

Decreasing

: \frac{5}{3} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = \frac{5}{3}

into

x^{3} - 7 x^{2} + 15 x + 9 : \frac{518}{27}

Maximum (\frac{5}{3}, \frac{518}{27})

Plug

x = 3

into

x^{3} - 7 x^{2} + 15 x + 9 : 18

Minimum (3, 18)

Maximum (\frac{5}{3}, \frac{518}{27}), Minimum (3, 18)

\frac{x ^{2}}{x}

f (x) = \frac{x ^{2} + 5 x - 6}{x + 3}

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

y = 4 x - 8

(1, 3), (4, - 3)

What is the extreme f(x)=x^3-7x^2+15x+9 ?
The extreme f(x)=x^3-7x^2+15x+9 is Maximum(5/3 , 518/27),Minimum(3,18)