What is the equation of the line normal to # f(x)=4x^2-3x-2 # at # x=3#?

1 Answer
Aug 20, 2016

#y=1/7 x+24 6/7#

Explanation:

Given:#" "f(x)=4x^2-3x-2#.......................Equation(1)

#=>f^'(x)=8x-3#

So the gradient of the normal will be #1/f^'(x)#

Thus we have #y=1/f^'(x) x+c #...........................Equation(2)
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#color(blue)("Determine the point on the curve at "x=3)#

#f(3)=4(3)^2-3(3)-2 =25#

Thus for the point #(x,y)->(3,25)# equation(2) becomes:

#25=1/(8(3)-3) (3)+c#

#c=25-1/7 = 24 6/7#

By substitution Equation(2) becomes:

#y=1/7 x+24 6/7#