For the function $f$, $f'(x)=2x+2$ and $f(2)=3$. What is the approximation for $f(2.1)$ found by using the line tangent to the graph of $f$ at $x=2$ ?

Summary Submit

First, write the equation of the tangent line at $x=2$.

$$f'(x)=2x+2$$ $$f'(2)=2(2)+2 = 6$$

Given a slope of $6$ and point $(2,3)$,

$$y-3=6(x-2)$$

At $x=2.1$,

$$y-3=6(2.1-2)$$ $$y-3=.6$$ $$y=\boxed{3.6}$$