Solve for: \text{begin}array l f(x)=13-x^2,

Expression: $\begin{array} { l }f\left( x \right)=13-{x}^{2},& \left( 3, 4\right)\end{array}$

Find the derivative of the function

$f '\left( x \right)=-2x$

To find the slope $m$ of the tangent line at $\left( 3, 4\right)$, find the value of the derivative for $x=3$

$f '\left( 3 \right)=-6$

The slope $m$ of the tangent line at $\left( 3, 4\right)$ is $-6$

$m=-6$

Write the tangent line in point-slope form using $\left( 3, 4\right)$ and $m=-6$

$y-4=-6\left( x-3 \right)$

Rewrite the equation in slope-intercept form

$y=-6x+22$