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amy0799
 one year ago
Find equations of the two tangent lines to the graph of f(x) = 2x^2 that pass through the point (0, 2).
line with positive slope:
line with negative slope:
amy0799
 one year ago
Find equations of the two tangent lines to the graph of f(x) = 2x^2 that pass through the point (0, 2). line with positive slope: line with negative slope:

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the equation of the tangent line, with slope m and which passes at the point (0,2), is: \[\Large y  \left( {  2} \right) = m\left( {x  0} \right)\]

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0I understand that, but how do I get the positive and negative slope?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I simplify that equation like below: \[\Large y = mx  2\] then I consider this algebraic system: \[\Large \left\{ \begin{gathered} y = mx  2 \hfill \\ y = 2{x^2} \hfill \\ \end{gathered} \right.\] I solve it, substitution method, namely I replace y into the second equation, by mx2, so I get this: \[\Large mx  2 = 2{x^2}\] now, in order to get the requested values for m, we have to request that the discriminant of that equation is equal to zero

amy0799
 one year ago
Best ResponseYou've already chosen the best response.0i found the derivative to be 4x. and plugging in 0 to 4x gets me o. so would the equations be: y+2=0(x0) y+2=0(x0)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I rewrite my last equation as below: \[\Large 2{x^2}  mx + 2 = 0\] which is a quadratic equation. Now I request that its discriminant, \Delta is equal to zero. \[\Large \Delta = {b^2}  4ac = {\left( {  m} \right)^2}  4 \cdot 2 \cdot 2 = 0\] Please, solve for m

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! nevertheless it is one solution, we have to find the second solution

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large {m^2}  16 = 0\] what is m?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1correct! your tangent lines are: y=4x2 y=4x2
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