Posted by Steven on .
The linearization at a=0 to sqrt(1+6x) is A+Bx where A is: ____ and where B is : ______

Calculus 
MathMate,
Let f(x)=sqrt(1+6x)
then f'(x)=3/sqrt(6*x+1)
and f'(0)=3
Thus the slope of the curve is 3 at x=0.
f(0)=1 means that the tangent to the curve passes through (0,1)=(x0,y0).
So the linearization is
y=Ax+B
=Slope(xx0)+y0
=3(x0)+1
=3x+1
Identify A and B for your answer.