Question

What is the maximum number of turns in the graph of this function?
f(x)=4x^3-12x^2-x+15

By turns, it means how many times the sign changes right? In which case it would be 1?

Answer 1

I think by turns it means peaks and valleys. The graph increases to a maximum and then turns around decreases to a minimum and then turns to become a maximum, etc.

Answer 2

So when it changes from an increasing function to a decreasing function it is a turn.
When it changes from an decreasing function to an increasing function it is a turn.

Answer 3

To find the critical points, that is possible local maxima / minima, we need to take the derivative. f(x) is a third degree polynomial. The derivative will be a second degree polynomial. When equated to zero to find the CPs, there will be two solutions. So the maximum number of turns (extrema) is 2.

Answer 4

Thank yhu. c:
Uhm , could yhu possibly help me write it out in an equation?