What is the equation of the line normal to f(x)=4x^2-3x-2 f(x)=4x2−3x−2 at x=3x=3?

1 Answer
Tony B
Aug 20, 2016

y=1/7 x+24 6/7y=17x+2467

Explanation:

Given:" "f(x)=4x^2-3x-2 f(x)=4x2−3x−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

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