Question

the line tangent of f(x) = 2X\(2X+1) is Y = 2X +1 at point (a,b) Find b

Answer 1

graph the function and the tangent line and see what the y-value of the tangent point is

Answer 2

The slope of the given tangent line is 2. Find out when \(f'(x)=2\):
\[f(x)=\frac{2x}{2x+1}\\
f'(x)=\frac{2}{(2x+1)^2}\]
Solve for \(x\) in the following equation:
\[\frac{2}{(2x+1)^2}=2\]
This \(x\) tells you when the slope of the tangent line to \(f\) is 2.