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Chapter 6: Q11. (page 291)

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

f(x)=x2-x-6

Short Answer

Expert verified

The minimum value of function is -6.25.

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)=x2-x-6

03

Step 3. Solution.

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

Here, a=1>0

So, the graph opens up and has a minimum value.

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

Thex-coordinate of the vertex is

鈭�b2a=鈭�(鈭�1)2(1)..........a=1,b=鈭�1=0.5

Find they-coordinate of the vertex by evaluating the function for x=0.5.

f(0.5)=0.52-0.5-6=-6.25

So, the minimum value of function is -6.25.

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