SOLUTION: Determine the slope of the tangent to y=1/1-x at the point (2,-1) without constructing a table. Explain what you are doing.
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Question 254184: Determine the slope of the tangent to y=1/1-x at the point (2,-1) without constructing a table. Explain what you are doing.
Found 2 solutions by drk, solver91311:
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
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)
and then
(ii)
Now put two into (ii) to get the slope at 2. We get
(ii) = 1.
So slope = 1 and passes through (2,-1)
Y = mx + b
-1 = 2*1 + b
b = -3.
answer:
Y = 2x - 3.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Take the first derivative of the function. Use the Chain Rule.
Let 
So:
by the power rule and
therefore
^2)
also by the power rule
and then, by the chain rule:
\ =\ \frac{dy}{dx}\ =\ \frac{dy}{du}\cdot\frac{du}{dx}\ =\ \left(\frac{-1}{\left(1\,-\,x\right)^2\right)\left(-1\right)\ =\ \frac{1}{\left(1\,-\,x\right)^2)
Then the slope of the line tangent to )
at )
is given by )
. In this case:
\ =\ \frac{1}{\left(1\,-\,2\right)^2}\ =\ 1)
John
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