wfg2.mw

restart; 1

WFG2

`:=`(f, proc (x) options operator, arrow; `+`(1, `-`(`/`(`*`(`+`(`*`(2, `*`(Pi)), `-`(`*`(2, `*`(arccos(`+`(x, `-`(1))))))), `*`(`^`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))))))), 2))), `*`(Pi)))) en...
`:=`(f, proc (x) options operator, arrow; `+`(1, `-`(`/`(`*`(`+`(`*`(2, `*`(Pi)), `-`(`*`(2, `*`(arccos(`+`(x, `-`(1))))))), `*`(`^`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))))))), 2))), `*`(Pi)))) en...

 

f(x) = `+`(1, `-`(`/`(`*`(`+`(`*`(2, `*`(Pi)), `-`(`*`(2, `*`(arccos(`+`(x, `-`(1))))))), `*`(`^`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))))))), 2))), `*`(Pi))))
x[min] = 0, x[max] = 1 (1)

`:=`(delta, proc (x) options operator, arrow; `/`(`*`(sqrt(`+`(`-`(`/`(`*`(diff(f(x), x)), `*`(`+`(1, `*`(`^`(diff(f(x), x), 2))))))))), `*`(C)) end proc); -1; 'delta(x)' = simplify(delta(x), size)

 

delta(x) = `+`(`/`(`*`(`/`(1, 40), `*`(`^`(40, `/`(1, 2)), `*`(`^`(`/`(`*`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))))))), `*`(Pi, `*`(`+`(`*`(`/`(1, 20), `*`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))...
delta(x) = `+`(`/`(`*`(`/`(1, 40), `*`(`^`(40, `/`(1, 2)), `*`(`^`(`/`(`*`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))))))), `*`(Pi, `*`(`+`(`*`(`/`(1, 20), `*`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))...
delta(x) = `+`(`/`(`*`(`/`(1, 40), `*`(`^`(40, `/`(1, 2)), `*`(`^`(`/`(`*`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))))))), `*`(Pi, `*`(`+`(`*`(`/`(1, 20), `*`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))...
delta(x) = `+`(`/`(`*`(`/`(1, 40), `*`(`^`(40, `/`(1, 2)), `*`(`^`(`/`(`*`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))))))), `*`(Pi, `*`(`+`(`*`(`/`(1, 20), `*`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))...
delta(x) = `+`(`/`(`*`(`/`(1, 40), `*`(`^`(40, `/`(1, 2)), `*`(`^`(`/`(`*`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))))))), `*`(Pi, `*`(`+`(`*`(`/`(1, 20), `*`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))...
delta(x) = `+`(`/`(`*`(`/`(1, 40), `*`(`^`(40, `/`(1, 2)), `*`(`^`(`/`(`*`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))))))), `*`(Pi, `*`(`+`(`*`(`/`(1, 20), `*`(cos(`+`(`*`(10, `*`(arccos(`+`(x, `-`(1))...		 (2)

 

(3)

`:=`(H1, proc (x) options operator, arrow; `+`(x, `/`(`*`(`+`(f(x), `-`(f(x[min])))), `*`(diff(f(x), x)))) end proc); -1

`:=`(R1, Optimization:-Maximize(H1(x), x = x[min] .. x[max])); -1; 'R[1]' = R1

 

R[1] = [2.57079632679492676, [x = 1.]] (4)

limit(diff(f(x), x), x = x[min])

 

undefined (5)

plot(f(x), x = 0 .. 1)

 

Plot_2d
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