value of the function at a point $t \in(a, b)$

value of the function at $t \in(a, b)$ such that $f^{\prime}(t)=0$

Slope of the tangent drawn to the curve $y=f(t)$ at a point $t \in(c, d)$

Slope of the tangent drawn to the curve $y=f(t)$ at a point $t \in(a, b)$

$\tan ^{-1}\left(\frac{2}{121}\right)$

$\tan ^{-1}(2)$

$\tan ^{-1}\left(\frac{1}{13}\right)$

$\frac{\pi}{2}$

2

4

6

8

monotonically decreasing function

monotonically increasing function

increasing in $(1, \infty)$ and decreasing in $(-\infty,-1)$

decreasing in $(1, \infty)$ and increasing in $(-\infty,-1)$