Expert: Ahmed Salami - 10/13/2009

Question
f(x)=x^2-3x+4, at P(2,2)

Answer
Hi Jen,
The tangent line through any point on f(x) has the same slope as that of f(x) at the point.
f(x) = x² - 3x + 4
The slope of f(x) at any point x is
f'(x) = 2x - 3
At (2,2)
f'(2) = 2(2) - 3
     = 4 - 3
     = 1
The slope of the line is 1 and it passes through (2,2). Its equation is therefore
y-2/x-2 = 1
y - 2 = x - 2
y = x

Regards