10 points to the first person that can solve this derivative problem WITHOUT the chain rule?

Question

Let f(x) = 3/(x - 1)

a. find the slope of the tangent to the graph of f at a general point xsub0.

b. use the result of part a. to find the slope of the tangent at xsub0 = 4

c. write the equation of the line tangent to the curve at xsub0 = 4

DO NOT USE THE CHAIN RULE PLEASE

we didnt learn it yet =P

thanks in advance!

Answer 1

From the definition of the derivative then:

f(x+h) = 3 / (x + h - 1)

f(x+h) - f(x) = 3 / (x + h - 1) - 3 / (x - 1)

= [3(x-1) - 3(x + h -1)] / [(x + h -1)(x - 1)]

= -3h / [(x + h -1)(x - 1)]

( f(x+h) - f(x) ) / h = -3 / [(x + h -1)(x - 1)]

limit as h->0 gives us:

f'(x) = -3 / [[(x + 0 -1)(x - 1)]

= -3 / (x-1)^2

Now that you have the derivative, you can do the rest.