Question

Let f be the function defined by f(x)=(4x-8)/(x^2+5x-14)

write an equation of the lien normal to the graph of f at x=1


how?

Answer 1

the line tangent to the graph at (x,y) has slope f'(x)

f'(x) = -4/(x+7)^2
f'(1) = -4/8^2 = -1/16

The line normal to f thus has slope +16

f(1) = 1/2

So, now we have a point (1,1/2) and a slope: 16

So, the line is

y - 1/2 = 16(x-1)