Question

Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 − 24x − 18x^2

Answer 1

First derivative gives the slope of the tangent at any point on the curve; equating it with zero gives us the value of x where the slope is parallel to x axis, i.e., an extremity of the curve.
Second derivative tells us whether the curve is open downwards or upwards. Negative value indicates that the curve is open downwards, which gives us Maxima at slope 0.