QUESTION:
considering the curve y=3x^2 - x. Using the equation for the normal line to a curve, find the coordinates of the closest point on the curve to the point (1,1).
Hint: The line passing through (1,1) and the closest point (x,y) to it on the curve is the normal line through curve at (x,y). Using the equation for the normal line, and the fact that it passes through (1,1), solve for (x,y)
HELPFUL EQUATIONS:
normal line to a curve: mN = - 1/m where mN is the slope of the normal and m is the slope of the curve at the intersection point.
f`(x) = 6x - 1 = m
not sure where to go with this?
p.s. this may not be my last question as I'm doing a 6 question assignment and this is question 2
considering the curve y=3x^2 - x. Using the equation for the normal line to a curve, find the coordinates of the closest point on the curve to the point (1,1).
Hint: The line passing through (1,1) and the closest point (x,y) to it on the curve is the normal line through curve at (x,y). Using the equation for the normal line, and the fact that it passes through (1,1), solve for (x,y)
HELPFUL EQUATIONS:
normal line to a curve: mN = - 1/m where mN is the slope of the normal and m is the slope of the curve at the intersection point.
f`(x) = 6x - 1 = m
not sure where to go with this?
p.s. this may not be my last question as I'm doing a 6 question assignment and this is question 2