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<p>Given that $p$ and $q$ are such that $-\frac{13}{7} \leq p \leq 4$ and $\frac{11}{2} \leq q \leq 9\frac{1}{4}$, find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $p + q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $q - p$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $pq$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $pq$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest possible value of $p^2 + q^2$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the greatest possible value of $p^2 + q^2$.</span></div></li></ol>

Given that $p$ and $q$ are such that $-\frac{13}{7} \leq p \leq 4$ and $\frac{11}{2} \leq q \leq 9\frac{1}{4}$, find

the smallest possible value of $p^2 + q^2$,

the greatest possible value of $p^2 + q^2$.

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