What is the equation of the normal line of $f(x)=5x^3+2x^2+x-2$ at $x=2$ ?

Question

1705 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-18T03:07:59

$x+69y=3314$

$f(2)=40+8+2-2=48$

The tangent line is: $y=kx+n$ , where $k=f'(x)$ . So,

$f'(x)=15x^2+4x+1$

$f'(2)=69 => k=69$

The normal line is: $y=k_1x+n_1$ , where $k_1=-1/k$ .

$k_1 = -1/69$

$48 = -1/69*2+n_1 => n_1 = 48+2/69 = 3314/69$

Finally,

$y=-1/69x+3314/69$ or

$x+69y=3314$

What is the equation of the normal line of f(x)=5x^3+2x^2+x-2f(x)=5x^3+2x^2+x-2 at x=2x=2?