1.        Given the point 4, 1; , which point on f(x) = sqrt(x); is the closest to it? 

restart;  

 

 

 

f := proc (x) options operator, arrow, function_assign; sqrt(x) end proc;  

f := proc (x) options operator, arrow; sqrt(x) end proc; (8.1.1)
 

with(Student[Calculus1]); -1 

 

 

Dist := proc (x) options operator, arrow, function_assign; sqrt(`+`(`*`(`^`(`+`(sqrt(x), `-`(1)), 2)), `*`(`^`(`+`(x, `-`(4)), 2)))) end proc;  

Dist := proc (x) options operator, arrow; sqrt(`+`(`*`(`^`(`+`(sqrt(x), `-`(1)), 2)), `*`(`^`(`+`(x, `-`(4)), 2)))) end proc; (8.1.2)
 


 

Dist(x);  

sqrt(`+`(`*`(`^`(`+`(sqrt(x), `-`(1)), 2)), `*`(`^`(`+`(x, `-`(4)), 2)))); (8.1.3)
 

 

[.969253149032939909, [x = 3.75792644178398]]; (8.1.4)
 

f(3.75792644178398);  

1.938537191; (8.1.5)
 

 

 

 

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