What is the extreme f(x)=x^3-3x^2-45x+22 ?

The extreme f(x)=x^3-3x^2-45x+22 is Maximum(-3,103),Minimum(5,-153)

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extreme f(x)=x^3-3x^2-45x+22

extreme points

f (x) = x^{3} - 3 x^{2} - 45 x + 22

Maximum (- 3, 103), Minimum (5, - 153)

Solution steps

f^{'} (x) = 3 x^{2} - 6 x - 45

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 3

into

x^{3} - 3 x^{2} - 45 x + 22 : 103

Maximum (- 3, 103)

Plug

x = 5

into

x^{3} - 3 x^{2} - 45 x + 22 : - 153

Minimum (5, - 153)

Maximum (- 3, 103), Minimum (5, - 153)

- 8 x^{3} + 24 x + 3

f (x) = 2 x^{4} - 36 x^{2} - 1, - 4 \leq x \leq 4

(x - 3) (x - 11)^{3} + 7, 7 \leq x \leq 13

x^{2} + 2 x + 9 y^{2} - 6 y + 2018

f (x, y) = \frac{x ^{3}}{3} - 3 y^{2} - \frac{x ^{2}}{2} + x y

What is the extreme f(x)=x^3-3x^2-45x+22 ?
The extreme f(x)=x^3-3x^2-45x+22 is Maximum(-3,103),Minimum(5,-153)