What is the extreme f(x)=-x^3+9x^2-15x+1 ?

The extreme f(x)=-x^3+9x^2-15x+1 is Minimum(1,-6),Maximum(5,26)

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extreme f(x)=-x^3+9x^2-15x+1

extreme points

f (x) = - x^{3} + 9 x^{2} - 15 x + 1

Minimum (1, - 6), Maximum (5, 26)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = 1

into

- x^{3} + 9 x^{2} - 15 x + 1 : - 6

Minimum (1, - 6)

Plug

x = 5

into

- x^{3} + 9 x^{2} - 15 x + 1 : 26

Maximum (5, 26)

Minimum (1, - 6), Maximum (5, 26)

(5.8) (- 6.2)

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

- \frac{4}{x ^{3} - 9 x}

f (x) = \frac{3 x}{x + 3}

f (x) = 10 x - 6

What is the extreme f(x)=-x^3+9x^2-15x+1 ?
The extreme f(x)=-x^3+9x^2-15x+1 is Minimum(1,-6),Maximum(5,26)