What is the extreme f(x)=x^3+3x^2-45x+4 ?

The extreme f(x)=x^3+3x^2-45x+4 is Maximum(-5,179),Minimum(3,-77)

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extreme f(x)=x^3+3x^2-45x+4

extreme points

f (x) = x^{3} + 3 x^{2} - 45 x + 4

Maximum (- 5, 179), Minimum (3, - 77)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 5

into

x^{3} + 3 x^{2} - 45 x + 4 : 179

Maximum (- 5, 179)

Plug

x = 3

into

x^{3} + 3 x^{2} - 45 x + 4 : - 77

Minimum (3, - 77)

Maximum (- 5, 179), Minimum (3, - 77)

f (x, y) = - 6 x + 5 y

f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} + 7 x + 11 y

f (x) = 2 x^{3} - 3 x^{2} + 4

2 x^{3} + 6 x y^{2} - 3 y^{3} - 150 x

f (x) = x^{3} - 2 x^{2} - 15 x + 10, - 2 \leq x \leq 0

What is the extreme f(x)=x^3+3x^2-45x+4 ?
The extreme f(x)=x^3+3x^2-45x+4 is Maximum(-5,179),Minimum(3,-77)