Question 1044364
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A curve passes through he point P(0,3.5) and is such that dy/dx=2-x. The normal to the curve at P meets the curve again at Q.

Find the coordinates of Q.
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Since you are Calculus, I will talk to you as to a Calculus person.


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1.  Since dy/dx = 2-x, y = {{{2x}}}- {{{x^2/2}}} + {{{C}}}, where C is a constant.

    Find C from the condition that y(0) = 3.5.  (Use the info about the point P).


2.  The normal to the curve at P is the straight line y - x = k, where "k" is a constant.   (Why ?)

    Find the constant "k" from the condition that the normal passes through the point P = (0,3.5).


3.  Now solve the system


        y = {{{2x}}}- {{{x^2/2}}} + {{{C}}},

        y - x = k


    to find the second intersection point Q.
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