What is the monotone f(x)=x^3-75x+3 ?

The monotone f(x)=x^3-75x+3 is Increasing:-infinity <x<-5,Decreasing:-5<x<5,Increasing:5<x<infinity

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Find Where Increasing/Decreasing Using Derivatives f(x)=x^3-75x+3

monotone intervals

f (x) = x^{3} - 75 x + 3

Increasing : - \infty < x < - 5, Decreasing : - 5 < x < 5, Increasing : 5 < x < \infty

Solution steps

f^{'} (x) = 3 x^{2} - 75

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 5,

Increasing

: 5 < x < \infty

Increasing : - \infty < x < - 5, Decreasing : - 5 < x < 5, Increasing : 5 < x < \infty

y = (x - 5)^{2} - 4

- (x + 1) (x - 1)^{2}

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

x

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

What is the monotone f(x)=x^3-75x+3 ?
The monotone f(x)=x^3-75x+3 is Increasing:-infinity <x<-5,Decreasing:-5<x<5,Increasing:5<x<infinity