Question

For the curve y = x^3 - 27x - 3, show that it is monotonic increasing for all values of x.

Thanks to anyone who helps

Answer 1

the slope at any point (x,y) is 3x^2-27

Clearly this is not always positive, namely for |x| < 3
For instance
y(2) = -49
y(3) = -57

go to any online grapher, and you will see this.
In fact, you know that