# Calculus

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

• Calculus -

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

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