MHB How to Find the Ordinate of P for Minimum AB in a Quadrant Curve?

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To find the ordinate of point P for minimum line segment AB in the curve y = 7 - x², the solution is 49/8. The tangent at point P intersects the axes at points A and B, which need to be minimized. Participants in the discussion emphasize the importance of showing prior attempts to solve the problem for better assistance. There are challenges in assembling the necessary equations for the tangent and intersections. The conversation highlights the need for clarity in problem-solving approaches to facilitate effective help.
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P is a point in the first quadrant on the curve: y = 7 - x2 . By P is drawn tangent to the curve, and A and B are points at which cut to the coordinate axes. Find the ordinate of P so that AB is minimum

Answer = 49/8
 
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What have you tried and where are you stuck? We do expect for people to show what they've tried so we have at least some idea where they are in the problem and how we can assist them to proceed...when you just post the problem, we have no idea how to best help you. :D
 
MarkFL said:
What have you tried and where are you stuck? We do expect for people to show what they've tried so we have at least some idea where they are in the problem and how we can assist them to proceed...when you just post the problem, we have no idea how to best help you. :D

ok If P (x0,y0)
the tangent must be yy0+xx0
the interception of the curve xith x axe is +/-sqrt7 and y = 7
I don't know how to assemble the equations
How can I proceed?
 
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