with(plots); -1 

Section 3.3 II #35 

`:=`(f, proc (x) options operator, arrow; `*`(x, `*`(sqrt(`+`(6, `-`(x))))) end proc) 

proc (x) options operator, arrow; `*`(x, `*`(sqrt(`+`(6, `-`(x))))) end proc (1)
 

`:=`(fp, D(f)) 

proc (x) options operator, arrow; `+`(sqrt(`+`(6, `-`(x))), `-`(`/`(`*`(`/`(1, 2), `*`(x)), `*`(sqrt(`+`(6, `-`(x))))))) end proc (2)
 

solve(fp(x) = 0, x) 

4 (3)
 

`:=`(fpp, D(fp)) 

proc (x) options operator, arrow; `+`(`-`(`/`(1, `*`(sqrt(`+`(6, `-`(x)))))), `-`(`/`(`*`(`/`(1, 4), `*`(x)), `*`(`^`(sqrt(`+`(6, `-`(x))), 3))))) end proc (4)
 

solve(fpp(x) = 0, x) 

8 (5)
 

But x = 8 isn't in the durn domain!!! 

 

fpp(1) 

`+`(`-`(`*`(`/`(21, 100), `*`(`^`(5, `/`(1, 2)))))) (6)
 

fpp(4) 

`+`(`-`(`*`(`/`(3, 4), `*`(`^`(2, `/`(1, 2)))))) (7)
 

plot(f(x), x = -5 .. 6) 

Plot_2d
 

Illustrating two different limits at infinity from the 10/17/13 Lecture. 

 

`:=`(g, proc (x) options operator, arrow; `+`(sqrt(`+`(`*`(`^`(x, 2)), `-`(`*`(9, `*`(x))), 2)), `-`(x)) end proc) 

proc (x) options operator, arrow; `+`(sqrt(`+`(`*`(`^`(x, 2)), `-`(`*`(9, `*`(x))), 2)), `-`(x)) end proc (8)
 

plot(g(x), x = 0 .. 500) 

Plot_2d
 

`:=`(h, proc (x) options operator, arrow; `+`(g(x), `*`(2, `*`(x))) end proc) 

proc (x) options operator, arrow; `+`(g(x), `*`(2, `*`(x))) end proc (9)
 

h(x) 

`+`(`*`(`^`(`+`(`*`(`^`(x, 2)), `-`(`*`(9, `*`(x))), 2), `/`(1, 2))), x) (10)
 

plot(h(x), x = -500 .. 0) 

Plot_2d