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Question: tangent a grahp of a function

Question:tangent a grahp of a function

toandhsp 300 Maple 14
student
January 04 2012
0

I have a problem:" Write the  equation of all lines passing through the point M(19/12,4) and tangent to the graph of the function f(x) = 2*x^3 - 3*x^2 + 5. I did the following:

restart; 
[> f:=x->2*x^3 - 3*x^2 + 5;                    

[> g:=x->k*(x-19/12)+4;

[> solve([f(x) = g(x), diff(f(x),x) = diff(g(x),x)],[x,k]);

[> h:=k->k*(x-19/12)+4;
[> seq(h(k),k = [0,12,-21/32]);
in this way, I have to enter the values ​​of k 
(k = [0,12,-21/32])  "by hand"  (not automatically). Is there another way,  automatically? Please help me. Thank you very much.
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