Question

y=(x-1)/(x-6)
Use the definition of the derivative to find the slope of the tangent line to the graph at the point (7, 6).

Answer 1

\[lim_{x->7}\frac{\frac{x-1}{x-6}-6}{x-7}\]

Answer 2

if you really want to use the definition, that is what you have to compute

Answer 3

\[lim_{x->7}\frac{\frac{x-1-6(x-6)}{x-6}}{x-7}\]

Answer 4

\[lim_{x->7}\frac{\frac{-5x+35}{x-6}}{x-7}\]

Answer 5

\[lim_{x->7}\frac{\frac{5(7-x)}{x-6}}{x-7}\]

Answer 6

\[=lim_{x->7}\frac{-5}{x-6}\]

Answer 7

replace x by 7 and get -5. this is the slope

Answer 8

it is easier just to find the derivative using the quotient rule and then plug in 7, but is finding it using the definition. once you have the slope use the point slope formula to get your line