For f(x) =(1+2x)^2, what is the equation of the line tangent to x =1 ?

1 Answer
Apr 21, 2018

The equation for the tangent line is

y=12x-3.

Explanation:

If

f(x)=(1+2x)^2, then

f'(x)=4(1+2x),

f(1)=[1+2(1)]^2=9, and

f'(1)=4(1+2)=12

The equation for the tangent line is

y=12x+b.

We can use the known point (1, 9) to find b.

9=12(1)+b

b=-3

The equation for the tangent line is

y=12x-3.