Extremums on HP 42S

[Albert Chan]

I think the function is y = sqrt(abs(x^3+2*x^2+4))

(x^3+2*x^2+4)' = 3*x^2 + 4*x = 3*x*(x+4/3)

To understand why extremum -4/3 is misssed, we need to understand how Secant method work.

Assuming plot is above x-axis:

From (x1,y1),(x2,y2), secant line locate the root at the x-axis, go up, to get y3.
Then, it uses (x2,y2),(x3,y3) to locate x4, go up, to get y4 ...

Extremum that shaped like a \(\bigcup\) may be located.
Extremum that shaped like \(\bigcap\) will not (new x's will move away from it)