# Write the equation of the line tangent to f(x) = tan x + 3 at (pi/4. 4)

Write the equation of the line tangent to $f\left(x\right)=\mathrm{tan}x+3$ at $\left(\frac{\pi }{4}.4\right)$
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$f\left(x\right)=\mathrm{tan}x+3$ at $\left(\frac{\pi }{4}.4\right)$
$y=f\left(x\right)=\mathrm{tan}+3$
$\frac{d}{dx}×f\left(x\right)=\frac{d}{dx}\left(\mathrm{tan}x+3\right)$
${f}^{\prime }\left(x\right)={\mathrm{sec}}^{2}x+0$
$\frac{dy}{dx}={\mathrm{sec}}^{2}x$
Slope $m=\frac{dy}{dx}={\mathrm{sec}}^{2}×\frac{\pi }{4}={\mathrm{sec}}^{2}\left(\frac{\pi }{4}\right)={\left(\sqrt{2}\right)}^{2}=2$
$\left(y–4\right)=2\left(x–\frac{\pi }{x}\right)$
$y=2x–\frac{\pi }{2}+4$
$y=2x–\frac{\pi +8}{2}$