Find the equation of the tangent line to the graph of f(x) = tan x at $\left( \frac { \pi } { 4 } , 1 \right)$ .
A) y = 2x + 1 - $\frac { \pi } { 2 }$
B) y = 2x - $\frac { \pi } { 2 }$
C) y = 2x - 1
D) y = 2x + $\frac { \pi } { 2 }$
E) none of these

Question

Quizplus · Accepted Answer

The derivative of $f(x) = \tan(x)$ is $f'(x) = \sec^2(x)$. At $x = \frac{\pi}{4}$, $f'(\frac{\pi}{4}) = \sec^2(\frac{\pi}{4}) = 2$. The equation of the tangent line is $y - f(a) = f'(a)(x - a)$, so substituting $a = \frac{\pi}{4}$ and $f(a) = 1$, we get $y - 1 = 2(x - \frac{\pi}{4})$, which simplifies to $y = 2x + 1 - \frac{\pi}{2}$.

Find the Equation of the Tangent Line to the Graph (π4,1)\left( \frac { \pi } { 4 } , 1 \right)(4π​,1)

Find the Equation of the Tangent Line to the Graph $\left( \frac { \pi } { 4 } , 1 \right)$