3. Given Use Explore to create a graph of the function and the corresponding tangent line at x = a; .  

> restart;
 

> f := proc (x) options operator, arrow, function_assign; `+`(`*`(A, `*`(`^`(x, 2))), `*`(B, `*`(x)), C) end proc;
 

Typesetting:-mprintslash([f := proc (x) options operator, arrow, function_assign; `+`(`*`(A, `*`(`^`(x, 2))), `*`(B, `*`(x)), C) end proc], [proc (x) options operator, arrow, function_assign; `+`(`*`(... (9.3.1)
 

> f(a);
 

`+`(`*`(A, `*`(`^`(a, 2))), `*`(B, `*`(a)), C) (9.3.2)
 

> (D(f))(a);
 

`+`(`*`(2, `*`(A, `*`(a))), B) (9.3.3)
 

> tanline := proc (x) options operator, arrow, function_assign; `+`(`*`(A, `*`(`^`(a, 2))), `*`(B, `*`(a)), C, `*`(`+`(`*`(2, `*`(A, `*`(a))), B), `*`(`+`(x, `-`(a))))) end proc;
 

Typesetting:-mprintslash([tanline := proc (x) options operator, arrow, function_assign; `+`(`*`(A, `*`(`^`(a, 2))), `*`(B, `*`(a)), C, `*`(`+`(`*`(2, `*`(A, `*`(a))), B), `*`(`+`(x, `-`(a))))) end pro... (9.3.4)
 

> plot([`+`(`*`(A, `*`(`^`(x, 2))), `*`(B, `*`(x)), C), `+`(`*`(A, `*`(`^`(a, 2))), `*`(B, `*`(a)), C, `*`(`+`(`*`(2, `*`(A, `*`(a))), B), `*`(`+`(x, `-`(a)))))], x = -10 .. 10);
 

Embedded component 

A 

Embedded component 

1 

B 

Embedded component 

2 

C 

Embedded component 

3 

a 

Embedded component 

4 

 

>