Profit Maximising output given output and cost

Question

A perfectly competitive firm has a quadratic cost function

$$C(q)= 3+7q+q^2$$

and given price for output is 14.

What is the maximum profit it can make?

Answer 1

Write down profit as function of $q$.

$$\Pi(q) = 14q - (q^2 + 7q +3)$$

Now differentiating w.r.t $q$ and equating to $0$ will give you the profit maximizing output.