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January 30, 2015

January 30, 2015

Posted by **Nick** on Saturday, March 31, 2012 at 1:19am.

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 8:35amWhy 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 h-26 , as h --> 0

= -26

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