Find the equation of the tangent line to the function `f(x)=x^2` at x=3

Expert Answers
lemjay eNotes educator| Certified Educator

First, solve for the value of y when x=3 to get the point of tangency.

`f(x)= x^2=3^2=9`

So, the point of tangency is (3,9).

Next, determine the slope of the line tangent to the given function at (3,9). To do so, take the derivative of f(x).

`f'(x)= (x^2)'`


Then, plug-in the value of x.


Hence, the slope of the tangent line is 6.

Since the tangent line contains the point (3,9), use the point-slope form to determine its equation.



Then, distribute 6 to x-3.


And, add 9 on both side of the equation to get y only.



Hence, the equation of the tangent line is `y=6x-9` .