normal means perpendicular
so if the 2 lines ar perpendicular then the slopes multiply to get -1
that means the derivitives multiply to get -1
let's call the first one f(x) and 2nd g(x)
f(x)=x²-7x
g(x)=-x+13
take derivitive of each
f'(x)=2x-7
g'(x)=-1
so when do they multiply to get -1
(2x-7)(-1)=-1
-2x+7=-1
minus 7 from both sides-2x=-8divide both sides by -2x=4
at x=4
so find the slope of f(x) then find the line perpendicular to it at x=3
f'(4)=2(4)-7=8-7=1
the slope is 1
the normal line will have a slope of -1 because 1 times -1=-1
find f(4)
f(4)=4^2-7(4)=16-28=-12
slope is -1 and a point is (4,-12)
y=-1x+b
-12=-1(4)+b
-12=-4+b
-8=b
y=x-8 is the equation
