min,max_f(x)
Author: Dani

Това е графика за илюстриране на НГС и НМС на квадратна функция в интервал.

The red segment corresponds to the interval  (m,n) of x 
in which you should find the  local extremum points (max and min).
the purple shows  the  corresponding function values.

Explore! 
Find the maximum and the minimum of the function:
 - for various values of the parameters with a fixed interval (m,n).
 - for various intervals and a fixed function.

a = -0.2999999999999998 (slider from -5 to 5, step 0.1)
b = -13.2 (slider from -20 to 20, step 0.1)
c = -3.8 (slider from -5 to 5, step 0.1)
f(x) = a x x + b x + c
A, B = Intersect(f, xAxis)
V = Extremum(f(x))
n = -34.2 (slider from -40 to 5, step 0.1)
m = 5.200000000000003 (slider from -20 to 20, step 0.1)
M: (m, 0)
N: (n, 0)
d = OrthogonalLine(M, xAxis)
e = OrthogonalLine(N, xAxis)
C = Intersect(f, d, (5.200000000000003, -80.55200000000004))
i = OrthogonalLine(C, yAxis)
D = Intersect(i, yAxis)
j = Segment(D, C)
E = Intersect(f, e, (-34.2, 96.74800000000018))
k = OrthogonalLine(E, yAxis)
F = Intersect(k, yAxis)
l = Segment(F, E)
p = Segment(M, N)
q = Segment(D, F)
r = Segment(C, M)
s = Segment(N, E)
t = OrthogonalLine(V, yAxis)
G = Intersect(t, yAxis)
a_1 = Segment(G, V)
GF = Segment(G, F)
GF1 = If(m < -b / (2 a), If[-b / (2 a) < n, GF])
GF2 = If(n < -b / (2 a), If[-b / (2 a) < m, GF])
g = If(m < x, If[x < n, f(x)])
h = If(n < x, If[x < m, f(x)])