Find the equation of the tangent line to the function `f(x)=x^2` at x=3
First, solve for the value of y when x=3 to get the point of tangency.
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).
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` .