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

The extreme f(x)=x^3-9x^2+15x+2 is Maximum(1,9),Minimum(5,-23)

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

extreme points

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

Maximum (1, 9), Minimum (5, - 23)

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 + 2 : 9

Maximum (1, 9)

Plug

x = 5

into

x^{3} - 9 x^{2} + 15 x + 2 : - 23

Minimum (5, - 23)

Maximum (1, 9), Minimum (5, - 23)

f (x) = (x^{2} - 1) e^{- x}

f (x) = - \frac{2}{3} x^{3} + 9 x^{2} - 28 x + 1

f (x) = ln (x^{2} + 4)

f (x) = x (25 - 40 + 2 x) (\frac{40}{2} - x)

f (x) = x^{\frac{1}{5}} (x + 12)

What is the extreme f(x)=x^3-9x^2+15x+2 ?
The extreme f(x)=x^3-9x^2+15x+2 is Maximum(1,9),Minimum(5,-23)