SOLUTION: please help me solve this question? Consider the function f(x) = -x2 + 3x - 1. Find the equation of the tangent to the graph of f(x) at x = 2. [NOTE: when calculating f'(2), use

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: please help me solve this question? Consider the function f(x) = -x2 + 3x - 1. Find the equation of the tangent to the graph of f(x) at x = 2. [NOTE: when calculating f'(2), use       Log On


   

Question 1183487: please help me solve this question?
Consider the function f(x) = -x2 + 3x - 1. Find the equation of
the tangent to the graph of f(x) at x = 2. [NOTE: when calculating f'(2), use
first principles.]
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
f%28x%29+=+-x%5E2+%2B+3x+-+1
Find: the equation of the tangent to the graph of f%28x%29+at x+=+2

f%28x%29+=+-x%5E2+%2B+3x+-+1
f'%28x%29=-2x+%2B+3
f'%282%29=-2%2A2+%2B+3=-1 => the slope of tangent line m=-1

f%282%29+=+-2%5E2+%2B+3%2A2+-+1=1

=> tangent point is at (2,1)

tangent line:
y-y%5B1%5D=m%28x-x%5B1%5D%29-> plug in m=-1 and (2,1)
y-1=-1%28x-2%29
y-1=-1x%2B2
y=+-x%2B3