Find an equation of the tangent line to the parabola $\displaystyle {y}={x}^{{2}}$ at the point $\displaystyle {P}{\left({2.1},{4.41}\right)}$.

Start by calculating the slope of the secant line $\displaystyle {P}{Q}$ for different points $\displaystyle {Q}$ that get closer to the point $\displaystyle {P}{\left({2.1},{4.41}\right)}$. Fill in this table similar to those in this example by calculating the slope of the tangent lines through $\displaystyle {P}$ and the point $\displaystyle {Q}{\left({x},{x}^{{2}}\right)}$ for the values of $\displaystyle {x}$ provided in the table.

$\displaystyle {x}^{{\text{}}}$	$\displaystyle {m}_{{{P}{Q}}}$
3
2.5
2.2
2.11
2.101
2.1001

Based on the values in this table, it appears the slope of the tangent line should be $\displaystyle {m}=$

Now that you have the slope $\displaystyle {m}$ of the tangent line and a point $\displaystyle {P}{\left({2.1},{4.41}\right)}$ on the tangent line, you can find the equation of the line:
tangent line is $\displaystyle {y}=$ Preview Question 6 Part 8 of 8