Find the coordinates of the point where the tangent to the curve at the point (2, 5) meets the normal to the same curve at the point (1, 2).
How can I solve this problem? Please help me.
You are probably wondering how Plato got those slopes.
Find the derivative of
Slope at is a simple plug and chug of the x-coordinate, so
Slope at is just , so the line normal to this point is perpendicular. Perpendicular slopes are opposite signed reciprocals, so that's how Plato got
let f(x) = ax^2 + bx + c.
set up three simultaneous equations. since (1,2) and (2,1) are on the curve, we have:
f(1) = 2 and f(2) = 1. so form two equations from that.
but there are three unknowns, we need at least three equations. so use the information from the derivative. we are also told that f ' (2) = 0, that's your third equation