Question

if f(x)= 4/(x-2), find f '(4)

Answer 1

think of it as 4(x-2)^-1, now differentiate using power rule
-4(x-2)^-2

Answer 2

technically chain rule as well but d/dx(x-2) = 1

Answer 3

so 1 would be my answer?

Answer 4

f'(x) = -4/(x-2)^2
f'(4) means you replace x with 4
=-4/(4-2)^2
=-4/4
= -1

Answer 5

oh, ok. Thanks. for this function, how would you calculate the slope of the tangent line at the point (4,2)

Answer 6

guess what you already did.
f'(4) is the slope the tangent line at (4,2)

Answer 7

crap, not slope. I meant intercept.