Posted by Anonymous on Saturday, October 23, 2010 at 12:24pm.
Determine the coordinates of the point on the graph of f(x)=sqrt(2x+1) where the tangent line is perpendicular to the line 3x+y+4=0
I do not seem to get the answer... I find the first derivative of f(x0 and equate it to the value of the slope from the tangent line. the answer says it should be (4,3) but i do not even get the xvalue correct.

Math  point on the graph (check +help)  Reiny, Saturday, October 23, 2010 at 1:33pm
my derivatiave is (1/2)(2x+1)^(1/2)(2)
= 1/√(2x+1) , that is the slope of the tangent.
slope of 3x+y+4 = 3
so the slope of the perpendicular is 1/3
then 1/√(2x+1) = 1/3
square both sides and crossmultiply
2x+1 = 9
x = 4
sub x=4 into original to finish