What is the equation of the normal line of $f (x) = \frac{x^{2}}{x^{3} - 5 x + 1}$ $f(x)= x^2/(x^3− 5x + 1)$ at $x = 5$ $x = 5$ ?

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Answer 1 · 2017-11-26T12:53:24

Equation of normal line is $y = 13.79 x - 68.7$ $y= 13.79x - 68.7$

$f(x)=x^2/(x^3-5x+1) :. f(5)=5^2/(5^3-5*5+1) ~~0.25(2dp)$

Point is at $(x_1,y_1) =(5,0.25)$ . Slope is $m= f'(x)$

$f'(x) = (2x*(x^3-5x+1)- x^2(3x^2-5))/(x^3-5x+1)^2$

$f'(x) =m= (25*(5^3-5*5+1)- 5^2(3*5^2-5))/(5^3-5*5+1)^2$ or

$m ~~-0.07$ . Slope of normal is $m_1= -1/-0.07~~13.79(2dp)$

Equation of normal line is $(y-y_1)=m_1(x-x_1)$ or

$(y-0.25)=13.79(x-5) or y= 13.79x - 68.7$ [Ans]

What is the equation of the normal line of f(x)= x^2/(x^3− 5x + 1)f(x)=x2x3−5x+1f(x)= x^2/(x^3− 5x + 1) at x = 5x=5x = 5?