Question

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

Answer 1

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 h-26 , as h --> 0
= -26