Expert: Ahmed Salami - 3/22/2010

Question
Find an equation for the tangent line to the graph of f(x)=squar.(x+1) at the point where x=3,
THE PROF. SAID THE ANS. should be x-4y=-5

Answer
Hi Dima,
The slope of the function f(x) = √(x+1) is given by
f'(x) = 1/2√(x+1)
At x = 3
f'(3) = 1/2√(3+1)
     = 1/2√4
     = 1/2(2)
     = 1/4
Also,
f(3) = √(3+1)
    = √4
    = 2
And so the equation of the line at the point (3,2) is given by
(y-2)/(x-3) = 1/4
4(y-2) = x-3
4y - 8 = x - 3
4y = x + 5
or
x - 4y = -5

Regards