Question 254184
The question was
Determine the slope of the tangent to y=1/(1-x) at the point (2,-1) without constructing a table.
step 1 - take the derivative of the function. We use the quotient rule to get
(i) {{{((1-x)*0 - 1*(-1)) / (1-x)^2}}}
and then
(ii) {{{1 / (1-x)^2}}}
Now put two into (ii) to get the slope at 2. We get
(ii) {{{1 / (1-2)^2}}} = 1.
So slope = 1 and passes through (2,-1)
Y = mx + b
-1 = 2*1 + b
b = -3.
answer:
Y = 2x - 3.