Slope of the normal to curve xy-3x+2y=6 at (3,2)?

1 Answer
Jim G.
Jun 24, 2018

#"slope of normal "=-5#

Explanation:

#"note that the slope of the normal is perpendicular"#
#"to the slope m of the tangent line"#

#m=dy/dx" at "x=2#

#color(blue)"differentiate implicitly with respect to x"#

#"differentiate "xy" using the "color(blue)"product rule"#

#xdy/dx+y-3+2dy/dx=0#

#dy/dx(x+2)=3-y#

#dy/dx=(3-y)/(x+2)#

#(3,2)tody/dx=(3-2)/(3+2)=1/5larrcolor(red)"slope of tangent"#

#m_(color(red)"perpendicular")=-1/m=-1/(1/5)=-5larrcolor(red)"slope of normal"#

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