Question

At $t=0$, the function $f\left(t\right)=\frac{sint}{t}$ has

• A. a minimum
• B. a discontinuity
• C. a point of inflection
• D. a maximum

Answer 1

The correct option is D a maximum

$f\left(t\right)=\frac{sint}{t}$$,f^{\prime }\left(t\right)=\frac{tcost-sint}{t^2}$
For critical points, $f^{\prime }\left(t\right)=0\therefore t=0$ where
$f^{\prime \prime }\left(0\right)=\frac{-1}{3}<0$
$\therefore f\left(t\right)$ is maximum at $t=0$