9.          Use the Tangent() function to determine the equation of a tangent line to f(x) = `/`(`*`(`^`(`+`(`*`(3, `*`(x)), 5), 2)), `*`(exp(x))); at x = -2.; Verify the solution with a plot.  

restart;  

f := proc (x) options operator, arrow, function_assign; `/`(`*`(`^`(`+`(`*`(3, `*`(x)), 5), 2)), `*`(exp(x))) end proc;  

f := proc (x) options operator, arrow; `/`(`*`(`^`(`+`(`*`(3, `*`(x)), 5), 2)), `*`(exp(x))) end proc; (6.9.1)
 

with(Student[Calculus1]); -1 

Tangent(f(x), x = -2);  

`/`(`*`(`+`(`-`(`*`(7, `*`(x))), `-`(13))), `*`(exp(-2))); (6.9.2)
 

 

Tanline1(x); (6.9.3)
 

plot([f(x), Tanline1(x)], x = -5 .. 10, y = -5 .. 100, color = [black, red]);  

Plot_2d
 

 

 

 

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