Posted by **Steven** on Friday, May 24, 2013 at 5:37pm.

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

- Calculus -
**MathMate**, Friday, May 24, 2013 at 7:31pm
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(x-x0)+y0

=3(x-0)+1

=3x+1

Identify A and B for your answer.

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