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Chapter 6: Q37. (page 291)

Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of the function.

f(x)=3-x2-6x

Short Answer

Expert verified

The function has maximum value that is 12.

Step by step solution

01

Step 1. Use the concept.

Consider the function f(x)=ax2+bx+c,a鈮�0 ,the x-coordinate of vertex is -b2a.

The graph of f(x)=ax2+bx+c,a鈮�0

  • opens up and has a minimum value when a>0, and
  • opens down and has a maximum value when a<0
02

Step 2. Given Information.

The given function is f(x)=3-x2-6x=-x2-6x+3

03

Step 3. Solution.

In the function f(x)=-x2-6x+3, we have a=-1,b=-6,c=3

Here, a=-1<0

So, the graph opens down and has a maximum value.

The maximum value of the function is the y-coordinate of the vertex.

Thex-coordinate of the vertex is

鈭�b2a=鈭�鈭�62(鈭�1)..........a=鈭�1,b=鈭�6=鈭�3

Find they-coordinate of the vertex by evaluating the function for x=-3.

f(-3)=--32-6-3+3=12

So, the maximum value of function is 12.

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