Question

Does a maximum value exist for y = 8x^2 + 80x + 72? Explain your answer.

Answer 1

Solution

Reason 1:

$\begin{gathered} y=8x^2+80x+72 \\ \\ \Rightarrow\frac{dy}{dx}=16x+80 \\ \\ \frac{d^2y}{dx^2}=16>0(\text{ Minimum\rparen} \end{gathered}$

Reason 2:

Since the coefficient of x is positive, the graph is going to be minimum.

Maximum value does not exist.