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

The extreme f(x)=x^3-9x^2+15x is Maximum(1,7),Minimum(5,-25)

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

extreme points

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

Maximum (1, 7), Minimum (5, - 25)

Solution steps

f^{'} (x) = 3 x^{2} - 18 x + 15

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 1

into

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

Maximum (1, 7)

Plug

x = 5

into

x^{3} - 9 x^{2} + 15 x : - 25

Minimum (5, - 25)

Maximum (1, 7), Minimum (5, - 25)

y = \frac{x ^{2} - 3 x - 4}{1 - 3 x - 4 x ^{2}}

\frac{20}{10 + e ^{x}}

3 x + 2 y = 10

x^{2} - 121

\frac{x}{x ^{2} - 16}

What is the extreme f(x)=x^3-9x^2+15x ?
The extreme f(x)=x^3-9x^2+15x is Maximum(1,7),Minimum(5,-25)