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.]

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(52847) (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".

RELATED QUESTIONS
Please help, Consider the function f(x) = x2 − 1. Find the equation of the... (answered by rothauserc)
please help me solve this question? Consider the function f(x) = -x2 + 3x - 1. Find the... (answered by MathLover1)
Find an equation of the tangent line to the graph of f(x)=(x^3+1)/(x^2+x+1) at the point (answered by richard1234)
Find an equation of the tangent line to the graph of f(x)=(x^3+1)/(x^2+x+1) at the... (answered by Fombitz)
The graph of the function f(x)= x-squared - 3. Find the slope of each of the tangent... (answered by stanbon)
Find an equation of the tangent line to the graph of f(x)=x^2-2x at... (answered by richard1234)
Please help me solve this problem: Let f be a quadratic function. The slope of the... (answered by Fombitz)
Consider the following function f(x)=x^2-sqrt x find the equation of the line tangent... (answered by Alan3354)
Find the equation of the tangent line to the graph of f(x)= 5-2 lnx at... (answered by ikleyn)