$f(t)$ has at least one local minimum.

$f(t)$ cannot have two distinct local minima.

$f(t)$ has at least one local maximum.

The minimum value of $f(t)$ cannot be negative.

$f(t)$ is not differentiable.

$f(t)$ is differentiable and its derivative is continuous.

$f(t)$ is differentiable but its derivative is not continuous.

$f(t)$ and its derivative are differentiable.

$t \, x(t) + \frac{dx(t)}{dt} = t^2 e^t$, $x(0) = 0$

$\frac{1}{2} e^t + x(t) \frac{dx(t)}{dt} = 0$, $x(0) = 0$

$x(t) \cos t - \frac{dx(t)}{dt} \sin t = 1$, $x(0) = 0$

$x(t) + e^{\left(\frac{dx(t)}{dt}\right)} = 1$, $x(0) = 0$

SCR

GTO

IGBT

Power MOSFET