Question

Now plug in your x =2 value inti the function rule to find your maximum and write it in the text box$f(x) = - 2x^{2} + 4x + 6$

Answer 1

$\begin{gathered} \text{Given f(x)= -2x}^2+4x+6 \\ \text{When x = 2, } \\ f(2)=-2(2)^2+4(2)+6 \\ f(2)=-2(4)+8+6 \\ f(2)=-8+8+6 \\ f(2)=6 \end{gathered}$

To find the maximum of the function:

From the graph, the maximum occurs at x = 1

We can also confirm using gradient at turning point idea to establish that the maximum of the function occurs at x = 1

$\begin{gathered} \text{ f(x)= -2x}^2+4x+6 \\ \text{Let y =-2x}^2+4x+6 \\ at\text{ turning point, }\frac{dy}{d\text{x}}=0\text{ } \\ -4x+4=0 \\ -4x\text{ = -4} \\ x=\frac{-4}{-4} \\ x=1 \\ \text{This shows the turning point, (a which is a maximum point is at x = 1)} \end{gathered}$

Substituting x= 1 into f(x), we have

$\begin{gathered} f(1)=-2(1)^2+4(1)+6 \\ f(1)=\text{ -2+4+6} \\ f(1)=8 \end{gathered}$

The maximum is 8