The function y = x 2 - 10x + 31 has a value of .

options for the first blank -
A. maximum
B. minimum
options for the second blank -
A. 31
B. 10
C. 6
D. 5

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

Step-by-step explanation:

In order to find the maxima or minima of a function, we have to take the first derivative and then put it equal to zero to find the critical values.

Given function is:

Taking first derivative

Now the first derivative has to be put equal to zero to find the critical value

The function has only one critical value which is 5.

Taking 2nd derivative

As the value of 2nd derivative is positive for the critical value 5, this means that the function has a minimum value at x = 5

The value can be found out by putting x=5 in the function

Hence,

The function y = x 2 - 10x + 31 has a minimum  value of 6

Hence,

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

x/3-10=8

x/3=18

x=48