Posted by Nick on Saturday, March 31, 2012 at 1:19am.
Find the equation of the tangent to the graph at the indicated point.
f(x) = x^2 − 1; a = 3
and
f(x) = x^2 − 8x; a = −9
whats the difference between 1 and 8x. What formula do I use and how should i solve both of these problems?
Thank you

Math  Reiny, Saturday, March 31, 2012 at 8:35am
Why are you using ""a , as in a = 3 ?
There is no "a" in either equation
Is this a "first principle" question to find the equation of the tangent to a curve ?
I will assume that is the case, and do the 2nd problem, the harder of the two .....
slope of tangent at x = 9 :
f(9) = 81 8(9) = 153
f(9 +h) = (9+h)^2 8(9+h)
= 81  18h + h^2 +72  8h
= h^2 26h + 153
slope
=lim [ f(9+h)  f(9) ]/h , as h > 0
= limit [ (h^2  26h + 153)  153]/h , as h > 0
= limit [ h(h  26 ]/h
= limi h26 , as h > 0
= 26
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