Help solving beginning calculus problem?

Question

[ f(a+h)-f(a) ] / h Have to use that limit formula

a) slope of the curve

b) an equation of the tangent, and

c) equation of the normal

y=x^2 - 4x at x=1

Do they same for this one

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

I did precalculus already but I forgot how do do these all I know is that the equation setup is like

[ f(a+h)-f(a) ] / h

Answer 1

[ -4(x+h)^2 - (x^2 - 4x) ] / h

use that, then take the limit as h goes to 0. You'll have to expand everything out so that you can cancel out some h's (so you don't divide by zero). Then when you take the limit as h goes to 0, the terms that still have h in them disappear and you're left with the equation of the tangent.

You should get y = 2x - 4

I forget how to do the equation of the normal.

Answer 2

dervi

y'=2x-4

slop=y'(1)=2(1)-4=-2

y=(1)^2-4(1)=1-4=-3

(1,-3) slop=-2

eq

(y--3)=-2(x-1)

(y+3)=-2x+2

y=-2x-1