Question

Is the selection I chose for the last question correct? And I need help with the first question if u don’t mind. Also this is from a homework practice

Answer 1

`\text{minimum ,4.5}`

Step-by-step explanation:

Firstly, we need to know if we will have a maximum or a minimum

This is dependent on the value of the coefficient of x^2, if positive or negative

This value dictates the direction in which the graph will face. The value is positive here, and that means the parabola will open up. This makes the extreme point a minimum

Now,let us get its value

We start by finding the first differential of the function

That would give:

`f^(\prime)(x)\text{ = 4x-6}`

Now, we equate this to zero and get the value of x

`\begin{gathered} 4x-6\text{ = 0} \\ 4x\text{ = 6} \\ x\text{ = 6/4} \\ x\text{ = 1.5} \end{gathered}`

Finally, we go back to substitute this value into the equation

We have this as:

`\begin{gathered} f(1.5)=2(1.5)^2-6(1.5)\text{ + 9} \\ f(1.5)\text{ = 4.5-9+9 = 4.5} \end{gathered}`