Answer the following True-False quiz. (Enter "T" or "F".)

 1. If [math] and [math], then [math] has a local minimum at [math].
 2. If a function has a local maximum at [math], then [math] exists and is equal to 0.
 3. If [math] for all [math] in [math], then [math] is decreasing on [math].
 4. A continuous function on a closed interval always attains a maximum and a minimum value.
 5. [math].
 6. Differentiable functions are always continuous.
 7. If [math] and [math] are increasing on an interval [math], then [math] is increasing on [math].