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

The extreme f(x)=x^3-3x^2-45x is Maximum(-3,81),Minimum(5,-175)

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

extreme points

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

Maximum (- 3, 81), Minimum (5, - 175)

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 : 81

Maximum (- 3, 81)

Plug

x = 5

into

x^{3} - 3 x^{2} - 45 x : - 175

Minimum (5, - 175)

Maximum (- 3, 81), Minimum (5, - 175)

f (x) = x^{3} + 3 x^{2} - 9 x - 5

f (x) = x^{2} - 12 x + 4

n^{3} + 2

2 x^{2} + 2

5 x^{2} ln (\frac{x}{4})

What is the extreme f(x)=x^3-3x^2-45x ?
The extreme f(x)=x^3-3x^2-45x is Maximum(-3,81),Minimum(5,-175)