SOLUTION: Consider the function f(x) = x 2 − 1. Find the equation of the tangent to the graph of f(x) at x = 3. [NOTE: when calculating f 0 (3), use first principles.]

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Question 1202241: Consider the function f(x) = x
2 − 1. Find the equation of the
tangent to the graph of f(x) at x = 3. [NOTE: when calculating f
0
(3), use first
principles.]
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
f(x) = x^2-1 x=3 find equation of tangent at x=3
Find the tangent point at x=3. Plug x=3
we get 3^2-1 =8
The tangent point is (3,8)
Find slope of x^2-1
dy/dx = 2x = 2*3 =6
y= mx+b equation of straight line
plug(3,8) and slope 6
8=6*3+b
b= 8-18
b=10
The equation of tangent
y = 6x -10
.

Answer by ikleyn(52835) (Show Source):
You can put this solution on YOUR website!
.

It is about finding the derivative of the given function,

and usually people solve such problems using standard rules of Calculus,

without using "first principles".