Question

Find all of the critical points of p (t). p (t) = t 2 + 5t + 6.

Answer 1

Please, use " ^ " to denote exponentiation: p(t) = t^2 + 5t + 6.

To find the critical points, differentiate p(t) with respect to t, set the result = to 0, and then solve the resulting equation for t:

p '(t) = 2t + 5 = 0

Solving for t: 2t = -5, and so t = -5/2. (-5/2, p(-5/2)) is the critical point. That evaluates to (-5/2, -0.25). This happens to be the vertex of a parabola that opens up.