What is the extreme f(x)=-x^3+12x^2-45x+2 ?

The extreme f(x)=-x^3+12x^2-45x+2 is Minimum(3,-52),Maximum(5,-48)

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extreme f(x)=-x^3+12x^2-45x+2

extreme points

f (x) = - x^{3} + 12 x^{2} - 45 x + 2

Minimum (3, - 52), Maximum (5, - 48)

Solution steps

f^{'} (x) = - 3 x^{2} + 24 x - 45

Find intervals:

Decreasing

: - \infty < x < 3,

Increasing

: 3 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = 3

into

- x^{3} + 12 x^{2} - 45 x + 2 : - 52

Minimum (3, - 52)

Plug

x = 5

into

- x^{3} + 12 x^{2} - 45 x + 2 : - 48

Maximum (5, - 48)

Minimum (3, - 52), Maximum (5, - 48)

f (x) = 2 - 4 x

(2, 5), (4, - 7)

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

f (x) = \frac{- 4 x - 6}{3 x - 2}

f (x) = 3 x^{2} - 10

What is the extreme f(x)=-x^3+12x^2-45x+2 ?
The extreme f(x)=-x^3+12x^2-45x+2 is Minimum(3,-52),Maximum(5,-48)