Question

nswer the questions below about the quadratic function.ƒ(x)=−2x² − 8x−7ya to aixs to nousupe--bзаtion 4 of 15Does the function have a minimum or maximum value?(-2,1)Where does the minimum or maximum value occur?of ma(2)7450 sintx=What is the function's minimum or maximum value?

Answer 1

Notice that the function is a second-degree polynomial.

a) Since the leading coefficient is negative, the graph of f(x) corresponds to a parabola on the plane that opens downwards.

Therefore, the function has a maximum value.

b) To find the minimum of f(x), solve the equation f'(x)=0, as shown below

$\begin{gathered} f^{\prime}(x)=0 \\ \Rightarrow-2(2x)-8=0 \\ \Rightarrow-4x-8=0 \\ \Rightarrow x=-2 \end{gathered}$

The minimum value of the function occurs at x=-2.

c) Then, the minimum value of the function is 1

$f(-2)=-2(-2)^2-8(-2)-7=-8+16-7=1$