Question

Which is the maximum value of the function y = −3x2 − 15x + 9?A.9B.27.75C.46.5

Answer 1

Solution

Step 1:

First find the first derivative and then equate it to zero to find x.

$\begin{gathered} \text{y = -3x}^2\text{ - 15x + 9} \\ \frac{dy}{dx}\text{ = -6x - 15} \\ -6x\text{ - 15 = 0} \\ -6x\text{ = 15} \\ x\text{ = }\frac{15}{-6}\text{ = -2.5} \end{gathered}$

Step 2:

Substitute x = -2.5 to find the value of y

$\begin{gathered} \text{y = -3x}^2-15x\text{ + 9} \\ \text{y = -3}\times(-2.5)^2-15(-2.5)\text{ + 9} \\ \text{y = -18.75 + 37.5 + 9} \\ \text{y = 27.75} \end{gathered}$

Final answer

Option B 27.75