A(n)=-4-2(n-1) find the 12th term in the sequence.
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The point (2, 5) is not on the curve; probably you meant to say (2, -5)?
Consider an arbitrary point Q on the curve to the right of P, , where
. The slope of the secant line through P and Q is given by the difference quotient,
where we are allowed to simplify because .
Then the equation of the secant line is
Taking the limit as , we have
so the slope of the line tangent to the curve at P as slope 2.
- - -
We can verify this with differentiation. Taking the derivative, we get
and at , we get a slope of
, as expected.
Let 
be the length of the hypotenuse in the right triangle 
, with 
for 
, the angle opposite the hypotenuse.
By the law of cosines,
But
, so we end up with 
.
By the law of cosines,
But